mems - based elements can be effective as an x - ray mirror only if the surface is atomically smooth and flat to efficiently reflect photons of ngstrom wavelength at grazing incidence angles ( without distorting ) the x - ray wavefront . to reveal whether mems mirrors possess these properties , we designed and fabricated torsional mems devices with a single oscillating element of single - crystal si ( 100 ) that is 10-m thick and 500-m  500-m in lateral dimension .
it is suspended by a pair of torsional flexures , which are anchored to the substrate , as shown in the scanning electron microscopy image ( fig .
the flexures allow the crystal to rotate in the torsional oscillation mode about an axis joining the anchors .
the device is fabricated using a soi ( silicon - on - insulator ) wafer that provides the single - crystal si layer necessary to diffract x - rays .
the substrate beneath the crystal is removed to allow large out - of - plane oscillations and to allow the transmission of x - rays .
the excitation is provided by in - plane comb - drive actuators , which are inter - digitated capacitors that provide torque with high force density121 ( see supplementary data 1 and supplementary fig .
the static x - ray reflectivity of the mirror at grazing incidence was measured while the device is not energized . with a two - dimensional x - ray detector ,
1b while the device was rotated from zero to the critical angle of the si mirror ( 0.18 ) .
the reflected beam was shown to be in well - defined spots indicating that the x - rays reflect off a high - quality mirror surface .
1c ) , which demonstrates the reflection efficiency predicted by theory14 . the measured reflectivity drops abruptly at the critical angle , again confirming a smooth and flat mirror surface . therefore
, the micromachined mirrors have comparable quality of conventional large x - ray mirrors and can be used to control the x - ray wavefront , for example , to optimally achieve x - ray focusing with an array of such elements and adaptive controls . as an x - ray diffractive optics , the mems crystal element also needs to be strain - free over the x - ray penetration volume to achieve high diffraction efficiency at both static and dynamic conditions . the x - ray rocking curve of the mems optics ( fig .
2a ) is measured with 8  kev x - rays around the si(400 ) bragg angle , b of 34.807 , using a high - resolution diffractometer ( see supplementary methods and supplementary fig .
it consists of a narrow and intense si(400 ) peak and additional intensity in the broad peaks above b .
these originate from the multiple lattice - strained surface - states due to shallow diffusive phosphorous dopant layers introduced on the crystal surface during the mems fabrication . besides a gaussian to fit the si(400 )
peak , the intensity profile was numerically fitted with two gaussian peaks centred at 0.0038 and 0.0091 above the si(400 ) peak , which agrees with a comprehensive investigation of phosphorous doped si22 .
the large angular separation of the shoulder peaks from the si(400 ) peak and their lower intensity allowed an accurate analysis of the si(400 ) peak .
2b ) , also modelled as a gaussian , has a full - width - at - half - maximum , (400 ) of 0.0034 ( 59  microradians ) . the above - described 3-gaussian analysis of the diffraction profile yields an extremely good fit to the measured data as shown in fig .
2b . we would , however , emphasize that the dopant - induced strain present in this device is due to the fixed multi - user mems fabrication process23 from the manufacturing foundry .
the stress due to the dopant layer is now well understood and has not interfered with our effort to optimize other parameters of the mems mirrors for dynamic x - ray optics .
the dopant effect can be eliminated in the future by using a custom foundry run . in the case of diffraction of a monochromatic beam ,
if the crystal were strain and defect free , the value of (400 ) would be determined by a convolution between the angular and energy widths of the incoming beam and the darwin width of the si(400 ) crystal ( ref .
the measured (400 ) is 20% broader , which can be accounted from the static deformation strain of the suspended 25-m thick mems crystal .
the static deformation of 0.0014 ( 24  microradians ) was estimated from the measured concave curvature of the crystal from both optical metrology and x - ray data . with the static deformation accounted for , the predicated rocking curve width of 0.0032 ( 55microradians )
the concept of using mems in the x - ray wavelength range as a dynamic diffractive optic for a monochromatic beam is shown schematically in fig .
a thin single - crystal si mems can diffract or transmit x - ray radiation just by a change in its relative orientation to the incident x - ray beam .
an oscillating mems device will diffract the x - rays over a short period of time when the bragg condition is satisfied and it will transmit the x - rays over the rest of the cycle .
3b , c that show , respectively , the incident 6.518-mhz x - ray pulses from the aps storage ring and a diffracted x - ray pulse when an incident 100-ps x - ray pulse struck the si mems and coincides with the si(400 ) bragg angle of the oscillating single crystal .
the x - rays pulses were measured with a fast - response avalanche photodiode detector operating in a charge - integrating mode ( see supplementary methods ) . the mems angular speed determines the width of the diffractive time window over which the bragg condition is fulfilled ( fig .
3d ) . varying the delay between the x - ray pulse and the instance when the crystal sweeps through its bragg angle can reveal the profile of the window in the time domain . to implement this concept successfully
, a mems device has to perform as an x - ray diffractive element with the highest reflectivity while maintaining this performance at high speeds without introducing any distortion to the incident wavefront .
here we demonstrate that these challenges for the mems to perform as a dynamic x - ray diffractive optics can be readily met , which unlocks innovative opportunities for their unique use as dynamic x - ray optics .
if the incident x - ray beam makes an angle 0 with the stationary si crystal , during the oscillation , the time dependence of the incident angle (t ) can be described as (t)=0+m cos ( 2fmt ) , where m is the amplitude and fm is the frequency of the mems oscillation .
the angular velocity of mems , (t ) , is given by where max=2fmm is the maximum angular velocity of the mems .
the incident x - ray beam is diffracted at the bragg condition , (t)=b , which occurs twice in an oscillation cycle .
4a , where t=1/fm is the oscillation period . for a crystal with a rocking curve width (hkl ) ( for diffraction plane hkl ) ,
the gap between two consecutive diffraction - windows ( in an oscillation cycle ) , tg , and the width of the diffraction time window , tw , are dependent on the angular offset between the mems equilibrium angle , 0 at the device resting position and the bragg angle b as =b0 ( see supplementary notes and supplementary fig .
3 ) , and are given by we shall emphasize here that  is not the incident angle , rather it is the parameter that we use to test the dynamic properties of the mems when the crystal is rotated away from its equilibrium ( or resting position ) by the motion of a diffractometer stage . from these equations
it can be noted that the smallest width of the diffraction time window , (hkl)/2fmm , is obtained when =0 ( when 0=b , the position where the resting crystal satisfies the bragg condition ) corresponding to a gap of 1/(2fm ) between the pulses .
the dynamic performance of the mems is evaluated from x - ray intensity measurements in the time domain from either a continuous - wave or pulsed x - ray source . in this study
we have used the incident x - ray pulse train from the advanced photon source 's standard operating mode in which the pulse - to - pulse separation is 153.4  ns ( ref .
the mems device was driven by a 70 vpp actuation signal with frequency 2fm ( fm=74.671  khz ) , resulting in a harmonic oscillation with a nominal amplitude m of ( )3 and period t of 13.392  s . during each mems oscillation cycle ,
only the x - ray pulses that satisfy the bragg condition arriving within the defined si(400 ) diffractive time window will be diffracted .
4 and is further discussed below . to validate the above concept , time dependence of the 8-kev diffracted x - ray intensities were collected for different offset angle 0 . by using the diffracted pulse intensity ( similar to that shown in fig .
3c ) , the profile of the diffractive time window is constructed by varying the arrival time of the x - ray pulses with respect to the mems driving signal . the measured profile in the time domain is shown in fig .
4b as a function of the angular offset =b0 . for every 0 , the bragg reflection is satisfied only during two short instances in each mems oscillation cycle . for clarity ,
4b are plotted in an expanded time scale by a factor of 20 to make their shapes clearly visible within the oscillation cycle .
the observed intensity profiles are mirrored on two branches of the oscillatory cycle , corresponding to the two instances in time when the bragg condition was met from two rotation directions .
the profiles with similar colours emphasize symmetrical performance of the mems in an oscillation cycle . along the vertical axis , the intensity peaks are offset by the amount of the offset angle  , ranging from 2.4 to + 2.0 , within the nominal oscillation amplitude of the mems .
the two critical dynamic parameters , tg and tw , can be derived from the position of diffraction peaks , as is illustrated in the figure .
4c as a function of the offset angle  , along with a fit ( solid line ) using equation 2 . the remarkable agreement between the data and the fit allowed accurate and independent determination of the mems oscillation amplitude , m=(2.690.01) , the only fitting parameter in the equation .
as reflected in equations 1 , 2 , 3 , this is the most critical parameter necessary to describe all the dynamic properties of the mems .
4b as a function of the offset angle  ( and the mirror images ) retain the features measured in the static rocking curve ( fig .
however the width of the si(400 ) peak varies with  ( or in time , tw ) ; in fact , it is inversely proportional to the angular velocity of the mems , as expected from equation 3 .
of all the peaks in the profiles , the narrowest and highest intensity peaks occur when =0 , at which the mems reaches the maximum angular velocity max=1.261  s .
the peak width reduces and intensity increases when the angular velocity increases as || decreases ( fig .
therefore , the time - domain diffraction profiles can be analysed with confidence using the same three - gaussian model to extract the width tw of the most prominent si(400 ) diffraction peak .
4d , along with calculated values ( solid line ) using equation 3 with no adjustable parameters . within experimental error ,
the data are adequately accounted for at =0 by equation 3 , without introducing additional strain - related broadening of the rocking curve , demonstrating negligible dynamic distortion of the mems at the x - ray bragg diffraction angle .
away from this angle , the measured value of tw departs rapidly from that predicted by equation 3 , suggesting that the additional broadening of (400 ) stems from a growing amount of strain introduced by dynamic deformation .
5a illustrates the surface profile of the mirror at the equilibrium position , where the averaged bending angle is minimal , especially the centre part of the crystal , perfectly supporting the x - ray measurement shown in fig .
4d . to highlight the narrowest diffractive time window achieved with the mems optic , the measured dynamic diffraction profile at =0
is shown in detail in fig . 5 , along with the fit introduced in fig . 2b , but in the time domain .
this is in excellent agreement with the value of 2.8  ns obtained from equation 3 using experimentally measured values of (400)=0.0034 , m=2.69 and fm=74.671  khz .
we should emphasize here that this minimal diffractive time window coincides with the angular range ( of about a degree , highlighted in fig .
4d ) where the mems oscillation does not cause any dynamic distortion in the si crystal , providing the opportunity of designing ultrafast but perfect crystal optics . even at large amplitude oscillations at 75 
khz , utilization of the bragg condition at the equilibrium positions of the oscillation cycle allows the crystal to maintain a perfect angular - temporal correlation , a characteristic necessary to use x - ray diffractive optics in temporal studies .
parenthetically we note that for one of the many capabilities possible , specifically the function of x - ray pulse selection has been attempted by non - mems - based methods with which the time window and repetition rate have been limited by the mechanical strength of the materials and peripheral velocity of the rotating element .
significant improvement of both the performance parameters simultaneously in a single device would be difficult and hence had never been demonstrated .
this was possible by miniaturizing the device to the realm of mems dimensions where scaling allows for the orders of improvement in both time window and repetition rate .
our results demonstrate the potential for mems technology in the x - ray wavelength range to control the x - ray beam and pulse train from an x - ray source .
the current device capability opens many new avenues for the use of mems to manipulate and control the spatial , temporal and spectral properties of x - rays similar to the functions demonstrated in the optical wavelength range .
single or an array of the mems elements can be used to perform fast scanning of x - ray beams and to manipulate x - ray wave fronts with adaptive controls such as in focusing applications .
the mems x - ray optics can disperse a well - tailored narrow bandwidth pink x - ray beam by maintaining a one - to - one spatiotemporal correlation with the x - ray energy .
this would provide unique opportunities to perform a new class of experiments such as fast time - domain x - ray spectroscopy even with densely filled electron bunches13 . as shown in fig .
4d , from =0.5 to + 1 ( shaded ) , where minimal dynamic distortion of the mirror is observed , this device can be used as a dynamic ( s ) monochromator or spectrometer . with this 1.5 of minimal - distortion range
, this device should be capable of dispersing x - rays with a bandwidth of < 2% and very high energy resolution ( < 1  ev ) for a densely spaced pulse interval in photon - energy domain ( 1  ev ) , suitable for near - edge spectroscopy experiments on microsecond time scales . using its dynamic diffractive capabilities , the present mems can readily be used to select an x - ray pulse or a stream of pulses , with a separation of over 2.8  ns and 150  khz at any hard x - ray storage ring with dense electron bunch filling patterns .
in addition , the x - ray fluence from this optic will be enhanced when applied to the ultra - small beam dimensions obtainable from the new generation of storage - ring sources with sub - nm - rad emittance25 .
the sources will provide much smaller and collimated x - ray beam after focusing and hence smaller ( even 10-s  m sized ) mirrors can be utilized . with reduced inertia and
increased flexure rigidity , faster mems can be achievable to significantly increase the performance of the x - ray mems optics .
other applications include those that are currently accomplished by bulk x - ray optics such as x - ray phase retarders26 and beam choppers for nuclear resonance scattering27 .
another interesting new capability would be to multiplex the x - ray pulses between multiple time - domain experiments at a synchrotron radiation or a high - repetition rate x - ray free electron laser ( xfel ) source .
future applications of mems x - ray optics hinge on their performance with increased speed ( operating at large amplitude in mhz range ) , small jitter ( ps ) , temperature stability and reliability for long - term operation .
fortunately , this is a well evaluated and proven area in photonics applications and can meet their immediate and the future use in x - ray applications discussed below .
the four control parameters for mems operation at =0 , namely b , (hkl ) , m , and fm , ( equations 1 , 2 , 3 ) allow for unprecedented capabilities .
they include : ( a ) the investigation of dynamic processes in a broad range of x - ray energies from 4 to 50  kev by choosing an appropriate b , ( b ) wafer - scale fabrication of mems making it economical to create a scalable catalogue of devices covering a broad range of operation frequencies and ( c ) the values of angular amplitude m can be varied by orders of magnitude either by varying the applied excitation voltage on mems28 or by varying the ambient pressure in which the device operates2930 .
this would provide flexible diffraction time windows to probe time scales at many mhz rates .
mems operation with larger values of m and fm will allow narrower time windows than the few nanoseconds reported here .
ultimately there is a potential to slice the x - ray pulses from a storage - ring synchrotron radiation source by several orders of magnitude to about few picoseconds .
conceived the project . the design of the mems torsional oscillators , fabrication and optical metrology was performed by d.m , i.w.j . and d.l .
the planning , execution and analysis of x - ray experiments at the advance photon source were performed by d.m .
all the authors were involved in the discussion of results and commented on the manuscript .
 photonic microsystems played an essential role in the development of integrated photonic devices , thanks to their unique spatiotemporal control and spectral shaping capabilities . 
 similar capabilities to markedly control and manipulate x - ray radiation are highly desirable but practically impossible due to the massive size of the silicon single - crystal optics currently used . here 
 we show that micromechanical systems can be used as x - ray optics to create and preserve the spatial , temporal and spectral correlation of the x - rays . 
 we demonstrate that , as x - ray reflective optics they can maintain the wavefront properties with nearly 100% reflectivity , and as a dynamic diffractive optics they can generate nanosecond time windows with over 100-khz repetition rates . since x - ray photonic microsystems can be easily incorporated into lab - based and next - generation synchrotron x - ray sources , they bring unprecedented design flexibility for future dynamic and miniature x - ray optics for focusing , wavefront manipulation , multicolour dispersion , and pulse slicing . 
Results
Discussion
Author contributions
Additional information
Supplementary Material