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11institutetext:  1 Physical Research Laboratory, Astronomy & Astrophysics
Division, Ahmedabad, India, 380009
Tel.: +91-79-2631-4401
Fax: +91-79-2631-4900
11email<EMAIL_ADDRESS>
22institutetext: 2 Indian Institute of Technology, Gandhinagar,India,382335
33institutetext: 3 _Present address:_ Government Senior Secondary School,
Hizrawan Khurd, Fatehabad, India, 125050

# Design and Development of Mt.Abu Faint Object Spectrograph and Camera –
Pathfinder (MFOSC-P) for PRL 1.2m Mt. Abu Telescope

Mudit K. Srivastava1 Vipin Kumar1,2 Vaibhav Dixit1 Ankita Patel1 Mohanlal
Jangra1,3 A. S. Rajpurohit1 S. N. Mathur1

(Received: date / Accepted: date)

###### Abstract

Mt. Abu Faint Object Spectrograph and Camera – Pathfinder (MFOSC-P) is an
imager-spectrograph developed for the Physical Research Laboratory (PRL) 1.2m
telescope at Gurushikhar, Mt. Abu, India. MFOSC-P is based on a focal reducer
concept and provides seeing limited imaging (with a sampling of 3.3 pixels per
arc-second) in Bessell’s B, V, R, I and narrow-band H-$\alpha$ filters. The
instrument uses three plane reflection gratings, covering the spectral range
of 4500-8500$\AA$, with three different resolutions of 500, 1000, and 2000
around their central wavelengths. MFOSC-P was conceived as a pathfinder
instrument for a next-generation instrument on the PRL’s 2.5m telescope which
is coming up at Mt. Abu. The instrument was developed during 2015-2019 and
successfully commissioned on the PRL 1.2m telescope in February 2019. The
designed performance has been verified with laboratory characterization tests
and on-sky commissioning observations. Different science programs covering a
range of objects are being executed with MFOSC-P since then, e.g.,
spectroscopy of M-dwarfs, novae $\&$ symbiotic systems, and detection of
H-$\alpha$ emission in star-forming regions. MFOSC-P presents a novel design
and cost-effective way to develop a FOSC (Faint Object Spectrograph and
Camera) type of instrument on a shorter time-scale of development. The design
and development methodology presented here is most suitable in helping the
small aperture telescope community develop such a versatile instrument,
thereby diversifying the science programs of such observatories.

###### Keywords:

Telescope Instrumentation Spectrograph Camera Optical Design

##  1 Introduction

The Astronomy and Astrophysics (A$\&$A) division of the Physical Research
Laboratory (PRL), Ahmedabad, India (under the aegis of Department of Space,
Government of India) operates the Mt. Abu Infrared Observatory (MIRO) at
Gurushikhar site (24.653 N, 72.779 E, 1680 m above mean sea level). MIRO
consists of a 1.2m Optical-Near Infrared (NIR) telescope equipped with a
variety of back-end instruments capable of studying the visible and NIR regime
of the spectrum. While the imaging observations in the visible range are being
provided by CCD/EMCCD Cameras, the imaging and spectroscopy in the NIR are
being done by the Near Infrared Camera and Spectrometer (NICS) (Anandarao et
al., 2008). In addition, a high-resolution echelle spectrograph – PARAS
(Chakraborty et al., 2014) has also been added to the suite of instruments for
exo-planet studies. All these instruments on the 1.2m telescope have been very
productive in producing results in diverse areas of astrophysics, e.g.,
studies of novae and supernovae (Srivastava et al., 2016; Joshi et al., 2017;
Banerjee et al., 2018a), Active Galactic Nuclei (Kaur et al., 2017), Comets
(Venkataramani et al., 2019), Binary systems (Chaturvedi et al., 2016),
detection of exo-planets (Chakraborty et al., 2018a), etc. To continue with
the tradition of observational research at PRL, the A$\&$A division is
establishing another 2.5m optical-NIR telescope at Mt. Abu (Pirnay et al.,
2018). The new telescope is expected to see first light in 2021. Four new
back-end instruments are being developed for the 2.5m telescope. This includes
a Wide-field Camera, a high-resolution spectrograph (Chakraborty et al.,
2018b), a NIR imager-spectrograph and an optical imager-spectrograph.

The optical imager-spectrograph for the 2.5m telescope was planned to be
developed along the line of the Faint Object Spectrograph and Camera (FOSC)
class of instruments. The FOSC series of instruments have been very successful
on various telescopes around the world (e.g., EFOSC on ESO 3.6m telescope
(Buzzoni et al., 1984), DFOSC on Danish 1.54m Telescope (Andersen et al.,
1995), FOCAS on 8.2m Subaru telescope (Kashikawa et al., 2000) etc.) as well
on several Indian facilities (e.g., IFOSC on IUCAA 2m telescope (Gupta et al.,
2002), HFOSC on IIA-HCT Hanle telescope (Prabhu and Anupama, 2010), ADFOSC on
ARIES Devasthal 3.6m Telescope (Kumar, 2016; Omar et al., 2017) etc.). A FOSC
type instrument has been one of the most sought after general-purpose,
versatile instrument on any small or medium aperture telescope, due to its
ability to provide imaging and spectroscopy in a single focal reducer based
optical chain. As the requirements of FOSC on the new 2.5m telescope were
being planned in late 2014, a similar instrument was also sought for the
existing 1.2m telescope. Various science programs of the astronomy group,
discussed above, required a facility for low/medium resolution spectroscopy in
the optical domain. Thus, as a precursor of a FOSC for the 2.5m telescope, we
decided to develop a pathfinder FOSC type instrument for the PRL 1.2m
telescope. This pathfinder instrument – named Mt. Abu Faint Object
Spectrograph and Camera-Pathfinder (MFOSC-P) - was planned to be a scaled-down
version of a typical FOSC, with a relatively smaller budget and development
period. MFOSC-P was thus designed and developed with a simple optical design
and with a commercially available off-the-shelf detector system. The above
choice of these two critical sub-systems led towards substantial design
innovation as compared to a typical FOSC type of instrument.

The design and development routes adopted for MFOSC-P are rather
unconventional for a FOSC kind of instrument. Some of the features of MFOSC-P
which make it a noteworthy development for the astronomical community; in
particular for the users of small aperture telescopes are as follows: a simple
optical design, relaxed opto-mechanical tolerances, use of an off-the-shelf
detector system and a robust control system based on commercially available
components. MFOSC-P has been successfully developed and commissioned on the
PRL 1.2m telescope in February 2019 after three and a half years of
fabrication and development. The success of MFOSC-P gives a boost to
instrumentation for small aperture telescope with limited financial resources.
In this paper, we describe the design and development of MFOSC-P, including
its optical design, opto-mechanical design, control system development along
with laboratory and on-sky characterization tests. We hope that these would be
of general interest to the community and enable replication (if so desired) on
similar telescopes around the world.

##  2 Science requirements and baseline design considerations

MFOSC-P was conceived to provide low/medium resolution optical spectroscopy
and imaging on the PRL 1.2m telescope and to supplement the ongoing
observational programs of the A&A division. Some of the long-term ongoing
programs of the division are NIR studies of novae and supernovae using NICS (a
hugely successful program), photometric studies of AGNs using CCD cameras, and
high-resolution spectroscopy studies of exo-planet/host star using the high-
resolution PARAS spectrograph. Thus, the baseline specifications of MFOSC-P
were derived from the science needs of such programs. The existing CCD camera
used for imaging is equipped with U, B, V, R and I band filters and mounted
directly in the telescope focal plane with a field of view (FOV) of $\sim$5.8
$\times$ 5.8 arc-minute2. NICS (the NIR imager/spectrograph)also has a similar
FOV and uses a 1K$\times$1K Hawaii image sensor for imaging. It provides
spectral resolution of $\sim$1000 in spectroscopy mode in $J$, $H$ and $K_{s}$
wavelength bands from 0.85–2.4 $\mu$m. Therefore, the desired imaging and
spectroscopy capabilities of MFOSC-P were chosen not only to complement these
existing programs but also to open up new areas of research like optical
studies of symbiotic stars. As mentioned in section 1, the novae and super-
novae programs, in particular, have extensively used the NIR spectrometer-
NICS. Apart from studies of the novae ejecta, understanding the physical
processes and astrochemistry of dust formation, etc., NIR spectroscopy has
also successfully provided a NIR classification scheme of early novae spectra
(especially useful for obscured novae which are faint in the optical but
bright in the NIR) (Banerjee and Ashok, 2012; Banerjee et al., 2018b). Optical
spectroscopy also usefully supplements the early classification of novae
spectra into the He/N or Fe II classes (Williams, 1992). Identification and
evolution of emission lines of various species in novae ejecta, the temporal
evolution of continuum, line profile variations seen in various emission lines
are useful diagnostics of the evolution of physical conditions in such
transient events. These lines cover the complete visible spectrum, e.g.,
hydrogen Balmer series including H-$\beta$ 4861$\AA$ and H-$\alpha$ 6563$\AA$,
low ionization lines of Mg I 5184$\AA$, Na I 5890$\AA$, O I $5577/7773/8446$
$\AA$ along with Fe II multiplets in Fe II class of novae, high excitation
lines of N III 4640$\AA$, He II 4686$\AA$, N II 5001$\AA$, N II 5679$\AA$, He
I 5876$\AA$, in He/N class of novae, etc. The spectral coverage and resolution
of MFOSC-P were thus determined from the requirements of such science cases.

A typical resolution of $\sim$5$\AA$ over the optical region was considered to
be adequate to address the scientific issues discussed above while ensuring a
good signal to noise ratio (SNR) over a range of magnitudes (see section
5.2.2). This resolution range is also suitable to study potential exo-planet
host targets like M dwarfs. A lower resolution of $\sim$10$\AA$ mode was also
incorporated for super-novae studies where the emission lines are considerably
broad (10,000 $kms^{-1}$ or more). This low-resolution mode was also required
to determine the spectral energy distribution (SED) over a broader wavelength
range. At the outburst, novae show broad lines with the full width at half
maximum (FWHM) of few thousand $kms^{-1}$, which in some cases (e.g.,
symbiotic novae (Srivastava et al., 2015)) decreases with time to few hundred
$kms^{-1}$. The evolution of the width and shape of the emission line profiles
in symbiotic systems carries significance in understanding the propagation of
shock waves into the dense ambient medium surrounding the white dwarf (Bode
and Kahn, 1985). To study such a scenario (among other possible ones), a
relatively higher resolution mode around H-$\alpha$ was also chosen with a
velocity resolution of $\sim 100-200$ $kms^{-1}$.

To minimize the cost of the instrument as well as to keep the
fabrication/development period within 2 to 3 years, it was decided to use
commercial off-the-shelf solutions for various components and sub-systems
wherever possible, e.g., detector system, gratings, filters, calibration
optics, motion controllers, etc. Gratings were chosen as the dispersive
element instead of grisms, which is a deviation from a customary FOSC design.
For similar reasons, a commercially available off-the-shelf CCD camera system,
along with its read-out electronics and data acquisition software, was decided
to be used in MFOSC-P. However, the use of such a commercial camera system
presented a constraint for the instrument’s optical system design. The image
sensors in these cameras are protected by a glass window in the vacuum
enclosures. The glass window is typically kept at a distance of 4-8mm from the
sensor. This spacing, as well as the external mechanical mounting
arrangements, put a constraint on the minimum distance of the last optical
surface of the optical chain from the image sensor. In the optical design of
most of the FOSC series of instruments, the last optical element is a
corrector lens for field curvature, which is kept close to the image sensor.
The distance between these two elements is usually kept small to reduce the
aberrations of the imaging system, e.g., field curvature for larger FOVs. It
is to be noted that a typical FOSC instrument provides a FOV of $\sim$11
$\times$ 11 arc-minutes2 on a 2K $\times$ 2K CCD and uses a field corrector
lens close to the image sensor(Gupta et al., 2002). We, nevertheless, adopted
a FOV of 5.2$\times$5.2 arc-minutes2 on a 1K$\times$1K CCD image sensor, with
a sampling scale of 3.3 pixels per arc-second (see section 3.2). The choice of
this FOV was consistent with our other existing instrumentation set-up (as
mentioned above) and did not require any field corrector lens for aberrations
control. It also allowed us to develop a simpler, cost-effective optical
design using only spherical singlet and doublet lenses. Further, given the
small aperture of the telescope and minimal throughput in the U band, the
instrument’s optical design was not optimized for the deep blue part or U band
of the spectrum.

Table 1: Design Parameters of MFOSC-P Parameters |  Values
---|---
Optimized Wavelength Range |  4500 – 8500 $\AA$
Imaging Field of View |  $\sim 5.2\times 5.2$ arc-minute2
Imaging Pixel Scale |  3.3 pixels per arc-second
Image Quality Requirement |  $\sim 80\%$ Encircled Energy Diameter is to be within 1.5 pixels
Magnification of the MFOSC-P optical Chain |  0.57
Camera F/Number |  7.4
CCD Detector |  1K $\times$ 1K ANDOR CCD with 13$\mu$m pixel size
Filters |  Astronomy standard Bessell’s BVRI filters. Narrow band H-$\alpha$ filter
Spectral Coverage of Gratings |  $\sim$4500-8500$\AA$ using three different Gratings
Spectral Resolutions $(\lambda/\delta\lambda)$ |  $\sim$2000, 1000 and 500 around 6500$\AA$, 5500$\AA$ and 6000$\AA$ respectively for 1 arc-second ($\sim 76\mu m$) slit width
Pupil Diameter |  $\sim$33 mm
Grating’s Specifications |  Three Plane reflection gratings, named R2000, R1000 and R500 with 500, 300 and 150-line pairs per mm blazed at $\sim$6500$\AA$, 5500$\AA$ and 6000$\AA$ respectively

Thus, MFOSC-P had been conceptualized to provide grating-based spectroscopy
and seeing limited imaging in standard Bessell’s B, V, R, and I filters. A
narrow band H-$\alpha$ filter had also been added to the design. The
wavelength range for the spectroscopy modes was chosen to be 4500-8500$\AA$,
which is sufficient to address the science goals, as described above. Three
plane reflection gratings with different groove-densities, viz. 500 line-pairs
(lp)/mm, 300 lp/mm, and 150 lp/mm (hereafter R2000, R1000, and R500 grating
modes respectively) were selected to cover this wavelength range. R2000
grating mode of MFOSC-P covers the wavelength range of $\sim$6000-7000$\AA$
with a resolution of $\sim 3.3\AA$. This corresponds to a velocity resolution
of $\sim$150 kms-1 around H-$\alpha$. R1000 grating mode has a resolution of
$\sim 5.0\AA$ over the wavelength range of $\sim$4500-6500$\AA$. This grating
can also be centred appropriately so that H-$\beta$ and H-$\alpha$ wavelengths
can be covered in a single exposure. R500 grating mode has the lowest
resolution ($\sim$12$\AA$) and the largest spectral range of $\sim
4500-8500\AA$ to provide SED and spectroscopy of broad lines astrophysical
objects. The optical design of MFOSC-P is discussed in the next section. Table
1 gives primary design parameters of MFOSC-P.

##  3 Optical and Opto-Mechanical Design

###  3.1 PRL 1.2m Telescope

MFOSC-P has been designed as per optical and mechanical requirements posed by
the PRL 1.2m telescope. The telescope is equatorial mounted. It consists of
1.2m primary and 0.3m secondary mirrors with the final f/13 beam at its focal
plane (Deshpande, 1995). The focal plane of the telescope can be adjusted by
motorized movement of the secondary mirror along the optics axis. MFOSC-P is
designed to be mounted on the Cassegrain port of the telescope through some
additional mounting arrangements. The telescope has a plate scale of 76 $\mu$m
per arc-second and aberration-free FOV of $\sim$10.0 arc-minutes of diameter
(Banerjee et al., 1997). The weight of the focal plane instrumentation is
typically restricted up to 125 kg. The physical space available beneath the
primary mirror cell for any instrumentation set-up is $\sim$1.0m diameter
$\times$ 0.8m depth. MFOSC-P was thus designed within such constraints of
volume, weight, and other mechanical parameters.

###  3.2 Optical Design of MFOSC-P

Like many of the FOSC instruments, MFOSC-P optical design is based on the
focal reducer concept. Such designs use the collimator-camera optical sub-
systems to map the telescope’s focal plane onto the CCD detector. The optical
chain provides a suitable magnification/de-magnification of the focal plane to
achieve a proper sampling of the seeing disc on the CCD. For the PRL 1.2m f/13
telescope, the seeing of 1.0 arc-second corresponds to 76$\mu$m on the
telescope focal plane. This seeing disc is to be sampled by at least 3 pixels
on the CCD plane. However, the imaging mode sampling scale of 3.3 pixels per
arc-second was chosen due to the gratings’ anamorphic magnification
($\sim$0.90-0.95)(Schweizer, 1979). In this way, a slit width of 1.0 arc-
second maps on to $\sim$3 pixels in the spectroscopy modes. As the pixels are
13$\mu$m $\times$ 13$\mu$m in size, the MFOSC-P optical chain has been
designed to provide a magnification of $\times$0.57 to achieve these sampling
scales.

Table 2: Parameters of the gratings used in MFOSC-P. All the gratings are
procured from Richardson Gratings (M/S Newport Corporation.)

Parameters |  | Values |
---|---|---|---
Grating Mode | R2000 | R1000 | R500
Catalog No. | 53-*-396R | 53-*-204R | 53-*-426R
Rulings (line-pairs per mm) | 500 | 300 | 150
Grating Order | 1 | 1 | 1
Blaze wavelengtha ($\AA$) |  $\sim$6500 |  $\sim$5500 |  $\sim$8000
Nominal blaze anglea (degree) | 11.1 | 4.7 | 3.4
Angle of incident (degrees) | 24.7 | 20.1 | 17.9
(with respect to grating normal) |  |  |
On-axis wavelengthb ($\AA$) |  $\sim$6510 |  $\sim$5730 |  $\sim$6520
Angle of Dispersion (degrees) | 5.3 | 9.9 | 12.1
(for on-axis wavelengths) |  |  |
Dispersion ($\AA$ per pixel) |  $\sim$1.1 |  $\sim$1.9 |  $\sim$3.8
Spectral range($\AA$) |  $\sim$5950-7100 |  $\sim$4700-6650 |  $\sim$4600-8450

  * a: As per manufacturer’s (Richardson Gratings, M/S Newport Corporation) grating specification sheets.

  * b: On-axis wavelengths for the given grating mode would fall in the centre of the detector in the spectral direction. For these, the sum of angles of incident and angle of dispersion would be 30 degree.

The optical design of MFOSC-P is shown in Figure 1. The optical design has
been developed in-house using only the spherical lens surfaces. ZEMAX Optical
Design Software is used for design purposes. The collimator section is
designed using a singlet lens and two cemented doublets lenses to produce a
collimated beam. It is kept at a distance of 148.5mm from the focal plane of
the telescope. The collimator optics forms the pupil image (diameter
$\sim$33.0mm) at a distance of about 385.0mm from its last lens element. As
discussed in section 2, three plane reflection gratings are selected from the
catalogue of M/S Newport Cooperation 111https://www.newport.com/b/richardson-
gratings; Accessed 2020-03-18. The important grating parameters, like the
blaze wavelengths, efficiencies, wavelength range, and dimensions, are found
suitable to be used within MFOSC-P. These gratings are used in the first order
to provide the slit-limited resolutions of $\sim$2000, 1000, and 500 at the
wavelengths of 6500$\AA$, 5500$\AA$, and 6000$\AA$ respectively. These
gratings and a fold mirror for imaging mode are mounted on the purpose-
designed turret-like mechanism. This mechanism is rotated by a stepper motor
so that the desired grating or mirror can be placed at the pupil position.
Optics axes of collimator and camera system are designed to be kept at an
angle of 30 degrees to reduce the effects of grating’s anamorphic
magnification(Schweizer, 1979). Thus, for the on-axis wavelengths of the
gratings modes (in the centre of the detector on the spectral axis), the sum
of angle of the incident ($\alpha$) and angle of dispersion ($\beta$) is fixed
at 30 degrees. Various parameters of gratings used in MFOSC-P are given in
Table 2.

Figure 1: The optical design of MFOSC-P. An additional fold mirror (not shown
in the figure) is also kept immediately after the last lens of collimator to
fold the design mechanically. Distances mentioned here are to show the scale
of the optical system. Exact values are given in Table 3. Figure 2: Poly-
chromatic imaging mode spot diagram of MFOSC-P optics at the detector plane,
for the design wavelength range 4500-8500$\AA$. Four radial field points are
chosen as top-left for on-axis (0,0) arc-minutes field, top-right for (1,1)
arc-minutes, bottom-left for (2,2) arc-minutes and bottom-right for (3,3) arc-
minutes field coordinates. Box size is 26 $\mu$m (2 pixels) a side. The CCD
detector has pixel size of 13$\mu$m a side in size and spans $\sim 5.2\times
5.2$ arc-minute2. The details of RMS spot diameters for various field points
are given in Table-4. Figure 3: Matrix spot diagram for R500, R1000 and R2000
grating modes of MFOSC-P. Box size is 26 $\mu$m (2 pixels) a side. The details
of RMS spot diameters for all the spectroscopy modes are given in Table-4.
Table 3: Lens Parameters for the MFOSC-P Optical Chain: This table contains
ZEMAX Optical Design Data

Element | Surface | Glass | Catalog | Radius of Curvature |  Thickness
---|---|---|---|---|---
|  |  |  | (mm) |  (mm)
|  |  |  |  |  (Distance to next Surface)
Collimator-Singlet-1 | First | N-PK51 | SCHOTT | -135.0 (CC)a |  12.0
Collimator-Singlet-1 | Second |  |  | -116.0 (CX)a |  37.0
Collimator-Doublet-1 | First | S-FTM16 | OHARA | 478.0 (CX) |  15.0
Collimator-Doublet-1 | Second | S-NSL36 | OHARA | 700.0 (CC-CX) |  15.0
Collimator-Doublet-1 | Third |  |  | 290.0 (CC) |  184.0
Collimator-Doublet-2 | First | S-FPL53 | OHARA | 286.0 (CX) |  21.0
Collimator-Doublet-2 | Second | S-NSL36 | OHARA | -115.6 (CX-CC) |  11.0
Collimator-Doublet-2 | Third |  |  | -307.0 (CX) |  510.0b
Camera-Doublet-1 | First | S-FPM3 | OHARA | 147.0 (CX) |  29.0
Camera-Doublet-1 | Second | S-BSM28 | OHARA | -93.3 (CX-CC) |  10.0
Camera-Doublet-1 | Third |  |  | Inf (Plano) |  96.8
Camera-Doublet-2 | First | N-KZFS4 | SCHOTT | -237.0 (CC) |  26.0
Camera-Doublet-2 | Second | K-GFK70 | SUMITA | 135.0 (CC-CX) |  12.0
Camera-Doublet-2 | Third |  |  | Inf (Plano) |  3.0
Camera-Singlet-1 | First | N-KF9 | SCHOTT | 136.8 (CX) |  15.0
Camera-Singlet-1 | Second |  |  | -218.8 (CX) |  63.0
Camera-Singlet-2 | First | N-LASF44 | SCHOTT | 90.4 (CX) |  11.7
Camera-Singlet-2 | Second |  |  | 205.3 (CC) |  12.1
Camera-Singlet-3 | First | S-LAH60 | OHARA | -102.0 (CC) |  10.0
Camera-Singlet-3 | Second |  |  | 185.0 (CC) |  29.65c

  * a : CC : Concave Surface. CX : Convex Surface. The intermediate surface of a doublet lens is described as CC-CX or CX-CC.

  * b : The 510.0mm (= 300.0+5.0+85.0+120.0 mm) is the distance between last surface of the collimator lens to first surface of camera lens. 300.0mm is the distance between collimtor to 5.0mm thick imaging filter, 85.0mm is from filter to grating and 120.0mm is from grating to camera lens surface.

  * c : The last distance from camera lens surface to the image sensor (29.65mm = 24.0+1.5+4.15 mm) is the distance from lens to the protective glass window (24.0mm), thickness of glass window (1.5mm) and from glass window to the image sensor (4.15mm).

A filter wheel, with Bessell’s B, V, R, I, and H-$\alpha$ filters, is placed
before the gratings in parallel beam space. The camera optics is placed at a
distance of 120mm from the pupil position after folding the beam. The camera
optics is designed with two doublet and three singlet lenses to produce an
f/7.4 beam. The image is finally recorded on 1024 X 1024 pixels CCD image
sensor with 13 $\mu$m pixel size. The detector system is an off-the-shelf
product (Model No. iKon-M934) from M/S Andor Technology
Ltd222https://andor.oxinst.com/products/ikon-xl-and-ikon-large-ccd-
series/ikon-m-934; Accessed 2020-03-18. It consists of a back-illuminated deep
depletion CCD and can be cooled to -80 degree C by using Peltier cooling. The
read-out noise is 3.3 electrons/pixel at the read-out rate of 50 kHz. The
distance between the CCD sensor and the last optical surface of camera optics
is optimized to be 29 mm for the reasons discussed in section 2. Off-the-shelf
slits from M/S Thorlabs and M/S Edmund Optics are used at the instrument’s
object plane. Two slits of 75 $\mu$m and 100$\mu$m width are used in MFOSC-P
for varying seeing conditions. The slits are 3mm in length, projecting on to
132 pixels at the CCD. Though the slits do not cover the entire length of the
CCD, they were found suitable for the spectroscopy of Galactic point sources
and extra-galactic bright super-novae. Given the moderate aperture of the
telescope, spatially resolved spectroscopy of extended diffuse sources are
usually not done with the telescope. The telescope is also not equipped with a
Cassegrain rotator to re-orient the slit. Thus, this off-the-shelf readily
available solution for the slits was adopted. Table-1 gives the baseline
design parameters of MFOSC-P. The details of optical design parameters, lens
specifications, glass types, etc. of the MFOSC-P optical chain are given in
Table 3.

###  3.3 Image Quality and Tolerances

MFOSC-P optics image quality requirement was to have the root-mean-square
(RMS) spot diameter within one-third of the seeing profile. For the desired
sampling of 3.3 pixels per arc-second and seeing of 1.0 arc-second, this
translates into an RMS spot diameter requirement of 1.1 pixels. The optical
system was thus attempted to design and optimize for RMS spot diameter around
$\sim$1.1 pixels, including various components and system tolerances, for all
imaging and spectroscopy modes. It must be mentioned that the final PSF on the
telescope focal plane also includes the contributions from the telescope
optics, its opto-mechanical arrangement, tracking system etc. These extra
factors further degrade the FWHM of the PSF on the telescope focal plane (see
section 5.2.1). Thus, the RMS spot diameter requirement of $\sim$1.1 pixels
truly corresponds to the telescope’s seeing limited performance. We,
nevertheless, choose this as the design criteria for the pathfinder instrument
as the newer upcoming 2.5m telescope would provide seeing limited performance,
and the next FOSC instrument for the new telescope would be designed with
similar criteria. The optics performance has been optimized for 8.0 arc-minute
diameter FOV in imaging mode. The wavelength range of 4500-8500$\AA$ is chosen
for the imaging and spectroscopy mode. The polychromatic spot diagram for
imaging mode is shown in Figure 2. Figure 3 shows the matrix spot diagram for
the spectroscopy modes. The other two spectroscopy modes have similar ray
footprints on the detector plane. Table 4 describes RMS diameters for all the
modes of imaging and spectroscopy. The throughput of the instrument is
estimated $\sim 30\%$ for spectroscopy modes. A throughput curve is shown in
Figure 4 for the instrument in R500 spectroscopy mode.

Figure 4: The throughput variation (solid thick dark curve) of MFOSC-P is
shown for R500 grating mode. Various contributors are shown in thin curves.
Grating response is for R500 grating. The other modes of spectroscopy have the
similar throughput profiles.

MFOSC-P optics has been designed to have loose tolerance values considering
the typical manufacturing capabilities of the optics manufacturers. Industry-
standard manufacturing errors of $\pm 25\mu$m /3 fringes on the radii of
curvatures and $\pm 50\mu$m on the lens elements’ thickness were considered
for the tolerance analysis. Two components of achromatic doublets were
required to be centred with accuracy better than 1.0 arc-minute. All the
lenses were coated with broadband anti-reflection coating with less than
$1.5\%$ reflectance over the wavelength range of 4500-8500$\AA$. Several other
optics specifications were chosen as per the requirement of scientific imaging
applications, e.g., power/irregularity of $4/1$, the surface quality of
$\lambda/4$ per inch, Scratch/Dig of 40/20, etc. In addition to component
level errors in the manufacturing, tolerances of $\pm 100\mu$m and $\pm$0.1
degrees were applied to the positioning accuracy and tilt of the individual
optics components, respectively, in their opto-mechanical arrangements. These
moderate values of tolerances for opto-mechanical imaging system development
are significant as it was decided to develop both the collimator and camera
lens barrel systems using in-house facilities.

MFOSC-P imaging performance has also been evaluated for its thermal analysis.
The typical observing conditions at the site ranges between 5 to 30 degree C
for most of the year. At a nominal temperature of 20 degrees C, the chromatic
focal range (for 4500-8500$\AA$) is determined to be within $\pm$130$\mu$m.
For the circle of confusion to be of 1.1 pixels diameter, the depth of focus
is determined to be $\pm$105$\mu$m, which is close to the focus range. For
temperature variation between 5 to 30 degree C, the focus shifts (for 4500,
6500 and 8500$\AA$) are found to be within $\pm$130 to 135$\mu$m which is also
comparable to the depth of focus. For the given temperature (5 to 30 degree C)
and pressure profile at the site, the corresponding RMS diameters are found to
be within 16$\mu$m, i.e. $\sim$1.2 pixels, for most of the field points (in
imaging mode) and spectral points (along the direction of dispersion in
spectroscopy modes). While this slightly overshoots the preferred seeing
limited criteria of 1.1 pixels, this performance was deemed acceptable due to
a broadened telescope’s PSF as explained above.

The above range of manufacturing and assembly tolerances and the thermal
conditions were incorporated in the final tolerance analysis of the MFOSC-P
optical chain using ZEMAX. The extreme range of temperatures variation from -2
to +35 degree C (and corresponding pressure values at Gurushikhar, Mt. Abu
site) was considered for this purpose. The statistical performance of
simulated systems using ZEMAX Monte Carlo analysis yields the mean of RMS spot
diameters within $\sim$1.1 pixels with a standard deviation of 0.3 pixels (for
all the modes of imaging and spectroscopy). The $90\%$ of the simulated
systems showed the RMS spot diameter values within 1.5 pixels. The back focal
distance of the camera optics was used as a compensator in the tolerance
analyses. Its variation was found in the range of $\pm$1.5mm for various
cases. This range was primarily useful to provide arrangements for a one-time
mechanical movement to the detector system while assembling the instrument in
the laboratory. Once the detector is mounted and aligned with the optics, any
further change in focus is expected to be due to a change in temperature only,
as discussed above.

Table 4: Image Quality Performance of MFOSC-P optical chain: RMS spot diameter
($\mu$m)

Imaging |  |  |  |  |
---|---|---|---|---|---
Radial Field Height | 0 | 1 | 2 | 3 | 4
(arc-minutes) |  |  |  |  |
Wavelength ($\AA$) |  |  |  |  |
4500 | 11.92 | 11.79 | 11.51 | 11.73 | 13.73
5500 | 9.98 | 10.34 | 11.68 | 13.64 | 15.86
6500 | 6.50 | 7.00 | 8.79 | 11.41 | 14.42
7500 | 2.94 | 2.52 | 2.37 | 4.32 | 7.61
8500 | 12.36 | 11.73 | 9.79 | 6.98 | 4.71
Spectroscopy |  |  |  |  |
Grating Mode | R500 |  | R1000 |  | R2000
Wavelength ($\AA$) |  |  |  |  |
4500 | 10.80 |  | - |  | -
5000 | 7.20 |  | 7.49 |  | -
5500 | 10.56 |  | 9.90 |  | -
6000 | 9.42 |  | 9.17 |  | 11.52
6500 | 6.29 |  | 8.06 |  | 5.98
7000 | 2.62 |  | 8.52 |  | 5.47
7500 | 2.46 |  | - |  | -
8000 | 6.16 |  | - |  | -
8500 | 9.90 |  | - |  | -

  * Note : Pixel Size is 13 $\mu$m a side.

###  3.4 Opto-Mechanical Design

A modular approach was adopted while designing the opto-mechanical sub-systems
of the instrument. In this scheme, various sub-systems were designed in a way
so that they could be assembled and characterized first on the laboratory test
bench set-up. These sub-systems were later assembled within the instrument’s
chassis plate. The collimator and camera optics were to align in their
respective barrels as per the assembly-integration-test (AIT) procedure. The
lenses were first mounted into their respective lens mounts and were checked
for their expected quality on a pre-designed imaging test bench set-up (see
section 5.1). In this case, simple on-axis optical imaging systems were
designed around each of the MFOSC-P lens/lens assemblies using off-the-shelf
lenses. The expected imaging performances were derived from the ZEMAX
simulations. The image quality for each of the lens assemblies was verified
before integrating them into respective barrels. The lens assemblies were
aligned and assembled into the barrels using a laser retro-reflection
technique. These collimator and camera optics barrels were then assembled into
a rigid cage-rod mechanical structure (see Section 5.1) to ensure the required
opto-mechanical tolerances as per designed AIT procedure.

Figure 5: Opto-mechanical system design of MFOSC-P instrument. Top panel (A)
shows the inner design and components of MFOSC-P. Panel (B) shows the outline
of the instrument, the inner enclosure for protection of the optics and the
outer enclosure. Panel (C) is the final configuration of MFOSC-P with its
support structure. Figure 6: Optical layout of MFOSC-P calibration unit. The
calibration unit is designed with off-the-shelf optical components to simulate
telescope’s f/13 beam. Telescope pupil is simulated by using a mask. See
section 3.4 for description.

The instrument enclosure is designed in the shape of the box consisting of a
10.0 mm thick L-shape chassis plate. All the opto-mechanical sub-assemblies
are mounted on this chassis plate. Figure 5 shows the schematics of the opto-
mechanical system design of MFOSC-P. The telescope beam enters into the
instrument through an optical protective glass window. The focal plane of the
telescope is formed inside the instrument. The slits are positioned on the
focal plane using a stepper motor based linear translational stage so that
they can be driven in and out of the optics axis. Due to the mechanical design
constraints, the field stop is mounted just below this translational stage at
the telescope focal plane to limit the FOV and stray light. The collimator
optical system then picks the beam from the focal plane and provides a
parallel beam space for the filters and gratings requirements. The linear
translational stage and collimator optics barrel are mounted on the vertical
plate of the L-shape chassis. A 45-degree fold mirror bends the parallel beam
in a horizontal plane. The beam passes through a stepper motor-driven filter
wheel with Bessell’s B-V-R-I-H$\alpha$ filters (50mm diameter) and an empty
slot for spectroscopy purposes.

The beam forms the pupil image after the filter on to the grating/imaging
mirror surface. Three different plane reflection gratings and a fold mirror
are mounted on the four faces (90 degrees apart) of a rotation mechanism
driven by a stepper motor. Desired grating (for spectroscopy) or mirror (for
imaging) can be brought into the path of the beam by rotating the mechanism.
The dispersed or reflected beam is directed into camera optics and forms the
image on the ANDOR CCD detector system. The filter wheel mechanism, gratings
motion mechanism, camera barrel, and the detector system are mounted on the
chassis’s horizontal plate.

Options for wavelength calibration of the spectra have been provided within
the instrument. A calibration unit has been designed and integrated with
MFOSC-P optics. It consists of an integrating sphere, two spectral lamps (Neon
and Xenon), a halogen lamp, and a re-imaging optical system. The pencil-style
spectral (Neon and Xenon) lamps from M/S Newport-Oriel are used for this
purpose 333https://www.newport.com/f/pencil-style-calibration-lamps, Accessed:
2020-03-18. The optical layout of the calibration unit is shown in Figure 6.
The lamps are coupled to the in-ports of the integrating sphere. The out-port
of the integrating sphere is re-imaged on the focal plane of the telescope
with a magnification of $\times$2.0. The re-imaging optics is designed using
two off-the-shelf achromat lenses (Thorlabs Part No.: AC508-075-A, 75mm focal
length, and Edmund Optics Part No.: 49-391, 150mm focal length) and two
mirrors to guide the calibration beam into the instrument. The first fold
mirror injects the calibration optics beam into the instrument through a glass
window. The second fold mirror is mounted on a stepper motor driven linear
translation stage on the vertical chassis plate, above the linear stage for
slit movement (Figure 5). This mirror blocks the telescope beam and feeds the
calibration beam into the main optics through the slit during the spectral
calibration. The second fold mirror is retracted during the science run of the
instrument. The telescope pupil is simulated by using a mask (12.0mm clear
aperture with a central obscuration of 2.7mm diameter) at the pupil location.
Thus, a telecentric $f/13$ beam is generated at the telescope focal plane. The
calibration unit optics was simulated with MFOSC-P optical chain in
spectroscopy mode to determine the centroid positions for the individual
wavelength spots. The centroid positions determined with MFOSC-P $+$
calibration unit optics design are in good agreement with those obtained from
MFOSC-P $+$ telescope optics design (within 2-3$\mu$m, i.e., $\sim 1/13$ of
spectral resolution in higher resolution mode of MFOSC-P). Figure 7 shows the
expected wavelength errors for all three modes of gratings. The centroids
positions of the emission lines of calibration lamps, obtained with the ZEMAX
model of calibration unit $+$ MFOSC-P optical chain, are fitted with a third-
order polynomial to obtain wavelength solutions. These wavelength solutions
were then compared with the centroid positions of individual wavelengths from
the ZEMAX model of telescope $+$ MFOSC-P optical chain to derived the expected
wavelength errors.

Figure 7: The expected errors in wavelength calibration, due to the use of
calibration unit optics, are shown for all the three grating modes.

MFOSC-P is also equipped with an off-axis guider system. Before the beam
enters into MFOSC-P, a 45-degree pick-up mirror selects an off-axis field and
directly image it on to Lodestar X2 auto-guider
camera444https://www.sxccd.com/lodestar-x2-autoguider; Accessed: 2020-03-19.
The 45-degree pick-up mirror and the Lodestar camera are mounted on a stepper
motor based motion mechanism. This mechanism allows movement of the auto-
guider system around 90 degrees along the periphery to scan the off-axis field
for a suitable guide star.

The instrument’s dimensions are 680mm $\times$ 608mm $\times$ 429mm, and it
weighs 68 kg. The opto-mechanical structure is made of aluminum (6061T) and an
inner enclosure is added for dust contamination. MFOSC-P is mounted on the
telescope along with its control system and control computer using a mild
steel support structure (Figure 5). The entire assembly weighs around 121 kg.
The finite element analysis of the MFOSC-P mechanical system (including its
external support cage system) was also done to ensure its structural integrity
and desired tolerances. Iterative analysis and structural modifications were
carried out to determine the most optimized configuration of the instrument’s
structure. The final design configuration was analyzed for self-weight load
and acceleration moments. Frequency analysis of instrument (first mode at 24.1
Hz and second mode at 36 Hz) showed that it is safely decoupled with the
telescope’s structure. Other structural analyses, like self-weight defections
in static and dynamic conditions, stress analysis, etc. were performed to
ensure compliance with the specified design requirements. The details of
structural analysis are described in Srivastava et al. (2018).

Figure 8: Block diagram of the hardware architecture of MFOSC-P control
system. Figure 9: The hardware set-up of MFOSC-P control system. Figure 10:
Block diagram of MFOSC-P control software architecture. Figure 11: The
graphical user interface (GUI) for MFOSC-P. The GUI has been developed using
Python-PyQT framework and acts as the font end of MFOSC-P control software.
See section 4 for details.

##  4 Automation and Control System

The automation and controls of MFOSC-P are provided in two parts: (1.) The
detector system controls, and (2.) the instrument operation controls. The
detector system has built-in read-out electronics. It is accessed through the
control software - SOLIS - provided by M/S/ Andor Technology Ltd
555https://andor.oxinst.com/products/solis-software/; Accessed: 2020-01-23.
This control software allows a variety of options for detector settings,
exposure times, and shutter controls. Different modes of data acquisition can
also be selected as per user’s requirements, e.g., sub-region selection,
different read-out speeds, image spooling and kinetic acquisition, etc. SOLIS
also has in-built features for detector cooling and protection. A variety of
image processing routines are also available for quick analyses of the data.
Other instrument operation controls of MFOSC-P are being provided by an in-
house developed instrument control system and graphical user interface (GUI).
MFOSC-P has five motion systems, viz. filter wheel, grating motion system,
slit $\&$ aperture positioning system, calibration mirror positioning system,
and the off-axis auto-guider pick-up mirror. All the motion systems are driven
by stepper motors or stepper motor based linear translational stages. Except
for the auto-guider system, all other motors are equipped with quadrature
encoders. Limits and home sensors are also used in all the motion systems.
These motion systems and the lamps in the calibration unit are being operated
through the instrument control system.

Though off-the-shelf solutions for motion controls are commercially available
(e.g., Newport motion controllers666https://www.newport.com/c/motion-
controllers. Accessed: 2019-09-05), they are generally restricted to two or
three axes only. Considering our long-term instrumentation requirements, we
decided to develop a general-purpose motion controller using commercially
available modules. Such a control system would provide the flexibility of
scaling up the number of axes as per the instrument’s requirements and would
be useful for multiple applications. Figure 8 shows a schematic block diagram
of the control system hardware set-up. The hardware of the control system
(Figure 9) is built around two ARCUS make PMX-4EX-SA series of motion
controllers. PMX-4EX-SA is an advanced 4-axes stepper stand-alone programmable
motion controller from ARCUS Technology, Inc.777https://www.arcus-
technology.com/ Accessed: 2020-01-23. It operates on a 24V power supply and
can be communicated with USB or RS-485 link. The controller can drive up to
four stepper motor drivers, including their encoders and limit/home sensor
feedback. It also has the provisions for digital input/output control signals
for some auxiliary tasks. In the control system, two ARCUS controllers drive
eight commercially available stepper motor drivers. These stepper motor
drivers can be individually configured in desired micro-stepping modes and for
the required current ratings of the stepper motors. From one of the
controllers, four of the digital outputs are used to control the operation of
calibration lamps through electro-mechanical relay-based control circuitry.
Four different power supplies 24V/10A-DC, 5V/4A-DC, 24V/10A-DC, and
24V/7.5A-DC from TRACO power supplies
888https://www.tracopower.com/home/;Accessed 2020-01-23 are used for
controller operations, relay circuit operations, limit sensor operations and
motor operations, respectively. While their input power is derived from mains
240V/50Hz AC, all these four power supplies are optically isolated with each
other in the control system.

The GUI software has been designed and developed to serve two functionalities
: (1.) To use the control system as a general-purpose 8-axes motion control
system for multiple purposes (2.) MFOSC-P specific user’s interface. GUI and
its application software have been developed using Python 2.7 with the PyQt4
framework. Figure 10 describes the block level architecture of the application
software. The front facade is the main front-end GUI window, which is designed
as per the requirements of the MFOSC-P instrument (see Figure 11). It provides
the visualization and status of various motion sub-systems. The progress of
any motion system while changing modes can be monitored on the GUI screen. The
front layer takes the user’s inputs/tasks. It then communicates to a general-
purpose engineering interface through an instrument-specific configuration
file and sub-system specific user interface layer. The configuration file is
stored in an editable ASCII text format and contains the default set-up status
of various sub-systems of MFOSC-P. It acts as the interface between the
instrument-specific main GUI screen and controller specific engineering
interface. Provisions are made in the front-end GUI to access the engineering
interface directly to access the hardware component (e.g., individual motors,
limit sensors, lamp control, etc.) separately for engineering tests and debug
purposes. The engineering interface is password protected and has another set-
up window to store each motor’s motion profile parameters (e.g., start speed,
top speed, acceleration, deceleration, pitch, micro-stepping mode, etc.). The
engineering interface window also provides access to a command-line console
interface, where one can directly interact with the controllers using the
ASCII command sets provided by controller’s manufacturers in the form of the
library functions. A USB communication layer then forms and sends the command
packet to the hardware system using the USB2.0 interface.

The software is designed to be platform-independent and easily scalable. The
main front window of the GUI is designed and configured as per MFOSC-P
requirements. However, the main GUI screen and configuration file can be
appropriately changed to make the software control suitable for any other
future instrumentation requirement while keeping the control system hardware
intact.

##  5 Characterization and Commissioning Performance

MFOSC-P was assembled and characterized in the laboratory from October 2018 to
January 2019. Performance verification of the optics components (e.g., lenses
and lens sub-assemblies), motion sub-systems testing, imaging and spectroscopy
performance verification, etc. were done in this period. Subsequently, MFOSC-P
was commissioned on the telescope in February 2019. Regular characterization
and preliminary science observations were made from February 2019 till June
2019. The laboratory and on-sky performance are described in the next sub-
sections.

###  5.1 Laboratory Characterization

####  5.1.1 Image Quality

The lenses were manufactured as per design by a commercial optics manufacturer
(M/S Gooch and Housego PLC, UK 999https://gandh.com/; Accessed: 2020-03-20)
and later assembled into the collimator and camera barrels in the laboratory.
The lenses were assembled into the barrels in a two-step process. First, each
of the lenses was mounted to their respective mounts. In some cases, two
lenses were designed to be kept very close to each other. These lenses were
housed in a single mount, thereby forming a lens system sub-assembly. These
mounts and sub-assemblies were later housed in the barrels. Before the
fabrication of the barrels, the primary optics specifications (e.g., focal
length) and lens quality of each of the lenses were checked by designing
individual test bench set-up for each of the lenses (or in some cases for lens
sub-assemblies) separately. Different on-axis imaging systems were designed
for the test bench around each of the MFOSC-P lens/lens assemblies. Commercial
off-the-shelf achromat doublet lenses were used for this purpose. An optical
fiber, of 10$\mu$m core diameter, was illuminated with Neon lamp at one side.
The output end of the fiber was imaged using the test set-up on a laboratory
quality SBIG camera system (Model No. STF-8300M, 5.4$\mu$m pixel size) with
the pre-determined magnification ratio. Narrow-band H-$\alpha$ filter and a
small aperture on pupil were also used in the set-up design to reduce
chromatic and geometric aberrations. The image quality was then measured and
compared with the expected performance determined with ZEMAX software. Figure
12 shows the one such set-up to verify the lens specification before its
assembly into the barrel. Though such schemes would only provide a good on-
axis image quality, they are found to be very useful in verifying the coarse
specifications of the lenses, in the absence of a costly wavefront analysis
set-ups like Interferometer.

Figure 12: The figure shows a test set-up designed to verify the basic optical
performance of individual lenses and lens assemblies. Panel (A) shows the
ZEMAX optical layout of the test set-up. This set-up was designed to provide
magnification of $\times$0.8 so that a fiber core diameter of 10$\mu$m would
fall within 1.5 pixels of the detector. Panel (B) shows the laboratory set up
as per the ZEMAX design. The spot diagram, simulated image and expected
profile of the fiber core are shown in panel (C). The recorded image of the
fiber core and resultant profile are shown in panel (D). SIBG camera with
5.4$\mu$m pixel size was used. The measured PSF was in good agreement with the
predicted ZEMAX performance. Similar set-ups were designed and verified for
each of the lenses and lens assemblies of MFOSC-P. Figure 13:  The figure
shows some aspects of assembly and integration of MFOSC-P. Panels (a), (b) and
(c) show the development of lens mounts and barrels. Panel (d) shows the
camera optics barrel under during development. The assembled lens barrels
including the optics for collimator and camera are shown in panels (e) and
(f). The final assembly of the instrument is shown in panels (g) and (h)
without outer enclosure cover plates. Figure 14: Image quality
characterization of MFOSC-P. Panel (A) displays the footprint of 10$\mu$m
pinhole illuminated with Neon lamp on the MFOSC-P CCD detector. Panel (B)
shows the counts recorded in central 3$\times$3 pixels for 10$\mu$m pinhole.
The mean background counts are 295. The FWHM of the PSF is estimated to be
$\sim 1.16$ pixels. Panel (F) shows the images of the standard test and
resolution target. It has grid structures of 100$\mu$m and 50$\mu$m, which
would correspond to pitch of 4.4 and 2.2 CCD pixels, respectively. Panels (D)
and (E) show these grid patterns. The grid patterns are well resolved by
MFOSC-P optics.

The mounted lenses were then assembled into collimator and camera optics
barrels using the laser retro-reflection method. ANDOR camera system was
integrated with the camera optics barrel assembly. Figure 13 shows some of the
aspects of the MFOSC-P AIT process. These optics sub-systems were evaluated
for the image quality assessment on the laboratory optical test bench before
integrating into the instrument chassis. The calibration unit optics
(discussed in Section 3.4) with Halogen, Xenon, and Neon lamps were used to
simulate the f/13 beam on the test bench. The image quality of the MFOSC-P
optical chain was characterized on the test bench with off-the-shelf pinholes
of various diameters (10, 25, 50 $\mu$m, etc.) and resolution test target from
M/S Thorlabs Inc101010https://www.thorlabs.com; Accessed: 2020-03-20 in
transmission mode. The pin holes were mounted on 2-D translational stages to
move it over the face of the CCD detector. As MFOSC-P optics provides
magnification of $\times$0.57, 10$\mu$m pinhole mapped onto 0.44 pixels of the
ANDOR camera system. Figure 14 shows some of the images obtained to estimate
the image quality of MFOSC-P optics. Panels (A) and (B) show the intensity
pattern of 10$\mu$m pinhole illuminated by Neon lamp without any filters. A
2-D Gaussian fits this pattern with FWHMs of 1.36 and 1.40 pixels in the X and
Y directions. A simple quadrature summation method is used to estimate the
Point Spread Function (PSF) of MFOSC-P optics. Thus, the geometrical
projection of the pinhole is removed from the measured FWHMs. The optics PSF
is determined as a Gaussian with FWHM of 1.16 pixels, which corresponds to
$\sim$80$\%$ encircled energy within 1.5 pixels. This result was consistent
with the results of opto-mechanical tolerance analysis, as discussed in
section 3.3. The PSF was then determined, for each of the B-V-R-I optical
filters, by imaging the pinhole at different coordinates on the face of the
detector. The measured PSFs are in good agreement with the predicted
performance of the optical design with tolerance analysis. The image quality
was also determined by using off-the-shelf resolution and distortion test
targets from M/S Thorlabs (Part No. R1L1S1N). The 100$\mu$m and 50$\mu$m grid
patterns, corresponding to the pitch of 4.4 and 2.2 pixels of the CCD
respectively, are well resolved by the MFOSC-P optics chain. The image of the
test target is shown in the panel (F) of Figure 14.

####  5.1.2 Spectroscopy Performance and Resolutions

MFOSC-P optics was also characterized in all the three spectroscopy modes
using lamps spectra with the calibration optics set-up. Figure 15 shows the
images and reduced spectra of Xenon and Neon spectral lamps using the slit of
75$\mu$m width. In all the cases, emission line profiles are well approximated
by the Gaussian function with FWHM of $\sim$3 pixels, which corresponds to
10.9, 5.7, and 3.2 $\AA$ for R500, R1000 and R2000 grating modes,
respectively. Figure 16 shows the profiles of these emission lines for R500,
R1000, and R2000 grating modes. Wavelength solutions for all the three
gratings are determined by using such spectra of the calibration lamps. A
third-order polynomial fit is used to determine the wavelength solutions.

Figure 15: Spectra of Xenon and Neon lamps used for wavelength calibration in
MFOSC-P. Figure 16: Line profiles for Xenon and Neon spectral calibration
lamps are shown. The central zero wavelength corresponds to Xenon lamp’s
7119$\AA$ line using R500 grating (Dots), Xenon lamp’s 5028$\AA$ line using
R1000 grating (stars), and Neon lamp’s 6506$\AA$ line using R2000 grating
(triangles). Gaussian fits to these lines result in $\sim$3 pixels FWHMs which
correspond to 10.9$\AA$, 5.7$\AA$ and 3.2$\AA$ for R500, R1000, and R2000
modes respectively. Figure 17: MFOSC-P instrument mounted on the PRL 1.2m
Telescope.

###  5.2 On-Sky Characterization

Several commissioning and science observations were made with MFOSC-P from
February to June 2019; till the onset of the monsoon season during which the
observatory is closed. A variety of targets were observed over these five
months and later after the monsoon season to ensure and confirm the
performance of spectroscopy and imaging modes. Figure 17 shows the final
mounting configuration of the MFOSC-P instrument on the PRL 1.2m Telescope.

Figure 18: Images of a region of M21 Open Cluster obtained by MFOSC-P in V
filter. A source of V magnitude $\sim$15.74 (encircled) is observed with an
error of 0.15 magnitude (SNR$\sim$7.3) in 40 seconds of integration time.
Figure 19: Slit profile of the 75$\mu$m slit recorded with diffused
illumination on the telescope dome floor. The instrument was mounted on the
telescope. The profile is well approximated by a Gaussian having FWHM of
$\sim$3.3 pixels. A section of the slit image is also shown in the inset.

####  5.2.1 Photometry

The imaging PSF of MFOSC-P is heavily dominated by telescope optics along with
the seeing profile of the site. On a typical night, the PSF was found to be
having FWHM of $\sim 2.3$ arc-seconds (measured using a separate CCD camera).
Figure 18 shows the image of a region of M21 open cluster observed in the V
band filter of MFOSC-P. The magnitude of one of the faint sources (encircled
in Figure 18) is determined to be 15.74 with the photometric error of 0.15
magnitude (corresponding to SNR of 7.3) in 40 seconds of integration time.

As the telescope PSF was not good enough to check the instrument’s PSF on the
telescope, we took the image of the 75$\mu$m slit in diffused dome lights
(with MFOSC-P mounted on the telescope) without any filter. The slit profile
is shown in Figure 19. A Gaussian fit results in FWHM of 3.3 pixels, which
ensure the intrinsic image quality of MFOSC-P on the telescope.

Figure 20: The plots show the expected SNRs from MFOSC-P for various V band
magnitudes, for all the three spectroscopy modes. The expected SNR (solid
circles) are obtained from a theoretical simulation model for 100 seconds
(dotted line), 300 seconds (dashed line), and 600 seconds (solid line) of the
simulated observations. The achieved SNR from MFOSC-P observations for varying
integration time, and various magnitudes are also shown in the solid
triangles. The corresponding integration times for each of the observations
are also mentioned, along with the data points. The achieved SNRs are in good
agreement with the predicted SNR values. See section 5.2.2 for details.

####  5.2.2 Spectroscopy Performance

A variety of objects, e.g., symbiotic systems, novae, M dwarfs, etc. were
observed with MFOSC-P over the last couple of years. There are described later
in this section. The instrument’s sensitivity was verified by comparing SNR
obtained with the MFOSC-P spectra of these sources with a theoretical
simulation model. The theoretical model assumes a seeing of 2.0 arc-seconds
FWHM, slit width of 1.0 arc-second, and the optics PSF as a Gaussian of
1-pixel FHWM. A flat V band spectrum was then simulated, incorporating the
total instrument efficiency (see Figure 4). The spectrum was convolved with
the slit profile function and then digitized using the gain of the CCD. The
spectrum was finally recorded against a laboratory recorded bias frame,
including the read-out noise, dark noise, etc. This simulated spectrum was
then extracted using the same aperture and algorithm, as in the case of
MFOSC-P observed spectra. The SNRs were determined for each pixel after
binning the data along the cross-dispersion direction within the aperture.
Figure 20 shows the SNR per pixel achieved with all the three modes of MFOSC-P
against their predicted values for sources of various magnitudes and exposure
times. The achieved SNRs are in good agreement with the predicted values. In
cases where the achieved SNR differs from the expected values, we expect
varying seeing conditions and the grating efficiency to be the main reasons
for the difference. The efficiency curves used in these simulations were
obtained from the manufacturer’s datasheet. The curves were generated for the
littrow configuration, which is different from the configurations used within
MFOSC-P. The stability of the instrument was verified by undertaking a long-
term science observing program of M Dwarfs after the instrument was
commissioned. Various subtypes of M Dwarf covering a range of magnitudes were
observed between February-June 2019. The spectra obtained were then compared
with their respective template spectra and later analyzed for their expected
outcomes. This program is discussed later in this section.

The on-sky throughput of MFOSC-P, including telescope optics and seeing, is
estimated by observing the objects from the list of spectro-photometric
standard
stars111111https://www.eso.org/sci/observing/tools/standards/spectra.html,
Accessed: 2021-02-21. In addition to the instrument’s intrinsic efficiency,
several other factors govern the final throughput. As discussed above, the PSF
at the telescope’s focal plane is dominated by the telescope optics and the
seeing profile, which causes the slit-loss. The reflectance of the telescope
optics (primary and secondary mirror) also degrades over time since their
aluminization. The grating efficiency curves provided by the manufacturer is
for the littrow configuration, which differs from the way gratings are being
used in MFOSC-P. We have incorporated the combined effects of all these
factors into the final ”seeing” PSF on to the MFOSC-P slit. Similar to what we
have done for comparing the SNR (in the above paragraph), we have simulated
the spectra of a standard star HD93521 ($V\sim 7$ magnitude), with the
efficiency curves discussed in section 3.3 and for the seeing of 2.0 arc-
seconds. This simulated spectrum was then compared with the observed MFOSC-P
spectrum to deduce the instrument efficiencies. Figure 21 shows the flux
calibrated spectrum of HD93521 in panel (a). The observed (solid curve) and
simulated spectra (dashed curve)) for R500 mode (for an integration time of 30
seconds) are shown in panel (b) in analogue-to-digital units (ADUs), without
any corrections. Only the continuum of HD93521 is simulated. The derived and
simulated efficiencies for R500 mode (solid and dashed curve, respectively)
are shown in panel (c) for comparison. The above process is also repeated for
R1000 and R2000 modes (for an integration time of 45 and 80 seconds,
respectively) and their efficiencies are compared in panel (d). It is seen
that the efficiency curve is well matched for the R1000 mode while deviating
for R2000 and R500 modes. This is due to the different nature of the grating
efficiency curves provided by the manufacturer (see Table 2). The efficiency
data used for R1000 grating is absolute for this grating in littrow
configuration. This has a peak efficiency of $\sim$62$\%$ at 5500$\AA$.
However, for R2000 and R500 grating, only relative values are given. Due to
which their peak efficiencies are higher ($\sim$87$\%$ and $\sim$80$\%$ at
6600$\AA$ and 6800$\AA$ respectively). As these grating efficiency curves are
used directly from the manufacturer’s datasheets, it causes the simulated
efficiencies to be higher for R2000 and R500 modes to generate the simulated
performance. The efficiencies of R2000 and R500 modes would also be in good
agreement with the derived ones if we consider the grating peak efficiencies
to be around 60$\%$ similar to R1000 modes.

Figure 21: Plots showing the on-sky efficiencies of the MFOSC-P as derived
from the observations. Panel (a) shows the flux calibrated spectrum of a
spectro-photometric standard star HD93521. Panel (b) shows the observed
spectrum of HD93521 with MFOSC-P R500 mode (solid line). The data is in units
of analog to digital units (ADU) as obtained from the CCD detector without any
efficiency correction. Dashed curve shows the simulated spectrum (only
continuum) of the star with MFOSC-P considering the seeing of 2 arc-seconds.
Panel (c) and (d) show the expected efficiency using simulated data (dashed
line) and derived efficiency using observations (solid line) of the instrument
for given seeing conditions for R500 and R1000/R2000 modes respectively. The
shaded regions in panel (b) and (c) show enhancement due to second order
contamination. See section 5.2.2 for discussion.

As discussed in Section 2, three modes of spectroscopy in MFOSC-P were
incorporated for varying purposes, viz. (a) to cover a broad spectral range to
determine the shape of SED (R500 mode), (b) to study the evolution of emission
lines in bluer part of the spectrum covering H-$\alpha$ and H-$\beta$ emission
in a single frame (R1000 mode), and (c) to check for the profile variability
of emission lines, in particular for the variability of H-$\alpha$ profile
(R2000 mode). These aspects have been verified using suitable targets over the
last couple of years since the commissioning of the instrument. Some of the
observations are described below.

(1.) Spectroscopy Observations of Symbiotics

The low/medium resolution optical spectroscopy has been of particular interest
in the studies of transient events like outbursts of symbiotic stars and
novae. The profile evolution of emission lines is a diagnostic tool to trace
the surrounding environment of a symbiotic system (e.g., Nova Sco 2015
(Srivastava et al., 2015)). The R2000 mode of MFOSC-P would be of particular
use for such cases. Two well known symbiotic stars/novae, T CrB and RS Oph
(Anupama and Mikołajewska, 1999), have been observed over the period with
MFOSC-P during the on-sky characterization phase.

T CrB was observed between 2019 and 2020. Figure 22 shows the MFOSC-P spectra
of T CrB in all the three gratings modes recorded in March 2020. The spectra
for 2019 and 2020 appear similar and show the same features as observed during
its 2015 super-active state (Munari et al., 2016). Strong emission lines of
high ionization species are seen on the top of a nebular continuum with
several absorption features of the M giant spectra. MFOSC-P spectra of T CrB
for 2019 and 2020 also show several emission lines like He II 4686$\AA$,
H-$\beta$, He I 4922$\AA$, He I 5016$\AA$ (blended with [O III] 5007$\AA$), He
I 5876$\AA$, H-$\alpha$, He I 6678$\AA$, and He I 7065$\AA$, etc. FWHMs of
H-$\alpha$ emissions are measured using R2000 spectra and found to be 7.1$\AA$
and 5.3$\AA$ for 2019 and 2020, respectively, including the instrumental
profile. The Equivalent widths (EW) of H-$\alpha$ and H-$\beta$ were estimated
after applying the reddening corrections of EB-V=0.048 (Munari et al., 2016)
to R1000 spectra. The EWs for (H-$\alpha$,H-$\beta$) are determined to be
(-36.5$\AA$,-19.0 $\AA$) for 2019 and (-49.6$\AA$, -28.1$\AA$) for 2020. These
measurements for T CrB are similar to those that were earlier reported by
Munari et al. (2016) and Iłkiewicz et al. (2016).

We have monitored the spectral evolution of RS Oph for few months. H-$\alpha$
emission in RS Oph is known to show line profile variability over the time
scale of a month (Zamanov et al., 2005). MFOSC-P spectra of Rs Oph also show
H-$\alpha$ profile variability between April and May 2019. Figure 23 shows
line profile variation seen in RS-Oph using the R2000 mode of MFOSC-P. The
profile shape and its variation are found to be consistent with the spectra of
RS Oph available in the public domain, e.g., ARAS (Astronomical Ring for
Access to Spectroscopy121212http://www.astrosurf.com/aras/; Accessed:
2020-04-12).

Figure 22: The spectra of T CrB, a symbiotic system, using all the three
spectroscopy modes of MFOSC-P. Figure 23: H-$\alpha$ variability observed in
the spectra of RS Oph. Figure 24: SDSS template spectra (blue) from Bochanski
et al. (2007) is compared with observed spectral sequence of M dwarf using
MFOSC-P (red).

(2.) Spectroscopy Observations of M-dwarfs

Along with the commissioning and characterization run of MFOSC-P, a science
program for the characterization of nearby M-dwarfs was undertaken during
February-June 2019. Bright M-dwarfs within 100pc with V magnitude less than 14
were selected from the all-sky catalogue of bright M-dwarfs (Lépine and
Gaidos, 2011). Selected sources cover the spectral types M0 to M5, which is
derived from the photometry. A total of 80 targets were observed for their
low-resolution spectroscopy using the R500 mode of MFOSC-P.

The spectra of these M dwarfs were compared with the SDSS standard M-dwarf
template spectra for their sub-classification. Figure 24 shows such a
comparison for a sample of M-dwarf spectra. The derived sub-spectral types of
M-Dwarfs in our sample ranges from M0-M5 with an error of one spectral
subclass. Later the spectral synthesis was performed on these spectra to
determine their fundamental stellar parameters, viz. effective temperature and
surface gravity. These stellar parameters of our sample targets were
determined by comparing the observed spectra with the synthetic spectra
generated by the BT-Settl model (Allard et al., 2013). The derived values of
effective temperature and surface gravity were in the range from 4000 K to
3000 K and 4.5 to 5.5 dex, respectively. This work has been published as a
first science result from MFOSC-P (Rajpurohit et al., 2020).

Figure 25: Low resolution spectrum of Nova AT2019QWF as recorded with MFOSC-P.
R500 grating mode was used with integration time of 300 seconds. The nova was
$\sim$16 magnitude in V band. Inset: Velocity plot showing H-$\alpha$ profile
of Nova AT2019QWF. This was observed with R2000 mode of MFOSC-P.

(3.) Spectroscopy of Nova AT2019QWF

Nova AT2019qwf was discovered by De et al. (2019) in a regular survey
operation of Palomar Gattini-IR (Moore and Kasliwal, 2019) on UT
2019-09-17.25. The nova was found to be highly reddened, and early
spectroscopy (Lee et al., 2019) determined the FWHM of the H-$\alpha$ line to
be 840 $kms^{-1}$. Optical spectroscopy of this nova using MFOSC-P was first
done on UT 2019-11-01.71. The spectra were recorded in the R500 and R2000
modes. The low-resolution spectrum showed a highly reddened continuum with
prominent H-$\alpha$ emission and OI lines at 7773$\AA$ and 8446$\AA$. The OI
7773$\AA$ line showed a P-Cygni profile with $\sim$14$\AA$ separation between
emission maximum and absorption minimum. FWHM and FWZI (full width at zero
intensity) of the H-$\alpha$ line were determined to be $\sim$340 $kms^{-1}$
and 2000 $kms^{-1}$, respectively from the spectrum obtained using the R2000
mode of MFOSC-P. Using the instrumental FWHM of 150 $kms^{-1}$ and quadrature
summation method, the intrinsic linewidth was found to be $\sim$300
$kms^{-1}$. Figure 25 shows the spectrum of the nova on UT 2019-11-01.71
obtained with the R500 mode of MFOSC-P with 300 seconds of integration time.
The velocity plot for H-$\alpha$ (as shown in the inset) was derived from the
spectrum obtained using R2000 mode. It is to be noted that nova was of
$\sim$16 magnitude in V band on the day of observations, as determined from
the AAVSO light curve (AAVSO - American Association of Variable Star
Observers131313https://www.aavso.org/; Accessed: 2020-03-20. The above has
been reported to the Astronomical Telegrams (Srivastava et al., 2019). The
nova observations for its spectroscopy evolution continued using MFOSC-P till
it went in conjunction with Sun in January 2020. Later, we also obtained the
spectra in May 2020 as it came out of the conjunction.

##  6 Summary

This paper presents the design and development details of MFOSC-P on the PRL
1.2m optical-NIR telescope at Mt. Abu. MFOSC-P has been developed as a
pathfinder instrument with an aim to develop the next generation FOSC type of
instrument for the upcoming PRL 2.5m telescope. The value of MFOSC-P lies in
its approach to have a simple, cost-effective optical design and development
methodology. Commercially available solutions were utilized in the development
of MFOSC-P, wherever possible. The main optical chain is designed as per the
requirements of the PRL 1.2m telescope. The optics has been designed with
readily available optical glass types and typical industry-standard tolerance
values. The overall opto-mechanical system, including the lens barrels, was
also designed with moderate tolerance ranges. The lenses of MFOSC-P optical
chain were fabricated by a commercial lens manufacturer, whereas the
mechanical parts were fabricated using in-house facilities. Other components
like filters, grating, slits, CCD detector system, etc. were chosen from
commercially available off-the-shelf solutions. Similarly, for the electronics
control system and software development, we relied on commercially available
products. This approach helped in shortening the project timeline, development
efforts, and in cost reduction.

The instrument was integrated and assembled in the laboratory using a simple
laser retro-reflection method. It was characterized in the laboratory on a
test bench set-up using various pinholes and test targets. MFOSC-P was
commissioned on the PRL 1.2m telescope in February 2019. A series of
commissioning and science observations were carried out from February 2019
till June 2019. The instrument has been used for a variety of science
observations since then, e.g., spectroscopy of M-dwarfs, novae, symbiotic
systems, H-$\alpha$ detection in star-forming regions, etc.

MFOSC-P has provided much-needed spectroscopy and multi-filter imaging
capability in the visible bands to the PRL 1.2m telescope. As PRL is gearing
up towards establishing another 2.5m optical-NIR telescope at Mt. Abu, lessons
learned from MFOSC-P are most valuable for the development of the next FOSC
instrument for the 2.5m telescope. The design and development approach adopted
here is well suited for any small aperture telescope/observatory, which often
requires a simple yet versatile instrument within a short period of
development. As the instrument has been successfully used for a range of
astronomical observations, the MFOSC-P presents a successful FOSC design,
which could be adapted with minimal necessary modifications on the similar
telescopes around the world.

###### Acknowledgements.

Development of the MFOSC-P instrument has been funded by the Department of
Space, Government of India through Physical Research Laboratory (PRL),
Ahmedabad. MFOSC-P team is thankful to the Director, PRL, for supporting the
MFOSC-P development program. We express deep thanks to D.P.K. Banerjee (PRL)
and Lalita Sharma (Indian Institute of Technology, Roorkee, India) for useful
comments on the manuscript. MKS expresses sincere thanks to Shyam N. Tandon
(Inter-University Center for Astronomy and Astrophysics – IUCAA, Pune, India)
for detailed discussions on several aspects of FOSC design throughout the
development process. VK is thankful to PRL for his Ph.D. research fellowship.
MFOSC-P team expresses sincere thanks to Mt. Abu observatory staff for their
sustained help and support during MFOSC-P commissioning and subsequent
observations. We thank the anonymous reviewer for useful comments and
suggestions.

## Conflict of interest

The authors declare that they have no conflict of interest.

## Funding

The development of the MFOSC-P instrument has been funded by the Department of
Space, Government of India through Physical Research Laboratory (PRL),
Ahmedabad.

## Availability of data and material

The instrument characterization data presented in this paper may be made
available on reasonable request.

## Code availability

Not applicable.

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