various embodiments of the invention are directed to methods , systems , and articles of manufacture for implementing multi - scenario physically - aware design of an electronic circuit design in a single embodiment or in some embodiments . other objects , features , and advantages of the invention are described in the detailed description , figures , and claims . various embodiments will now be described in detail with reference to the drawings , which are provided as illustrative examples of the invention so as to enable those skilled in the art to practice the invention . notably , the figures and the examples below are not meant to limit the scope of the present invention . where certain elements of the present invention may be partially or fully implemented using known components ( or methods or processes ), only those portions of such known components ( or methods or processes ) that are necessary for an understanding of the present invention will be described , and the detailed descriptions of other portions of such known components ( or methods or processes ) will be omitted so as not to obscure the invention . further , various embodiments encompass present and future known equivalents to the components referred to herein by way of illustration . as discussed in u . s . provisional application ser . no . 61 / 909 , 774 ( now u . s . patent application ser . no . 14 / 555 , 585 ); u . s . pat . nos . 6 , 046 , 720 ; 7 , 555 , 333 , 784 , 697 ; and u . s . patent applications ser . nos . 11 / 573 , 118 and 12 / 468 , 832 , each of which is incorporated by reference herein in its entirety , a variable focus element ( hereinafter “ vfe ”) may be used to adjust the wavefront ( e . g ., focus ) of an image in a dynamic fashion , and may be used to generate multi - focal 3d imagery . the vfe may enable analog focus modulation , or may switch between discrete focus states . this disclosure describes the use of a plurality of switchable screens , such as switchable polymer dispersed liquid crystal ( hereinafter “ pdlc ”) diffusers to spread incident light , such as for the purpose of increasing the effective numerical aperture of an image and / or increasing the size of an eyebox or exit pupil of viewing optics . for instance , a pdlc screen can be switched between a substantially transparent state and a substantially diffusing state . the plurality of switchable screens is , in preferred embodiments , operatively coupled to one or more vfes that can adjust the wavefront of light incident upon a switchable screen . for brevity , the rest of this disclosure refers to a singular vfe , but it is to be understood that a plurality of vfes can be used in the stead of single vfe in each of the embodiments . in one embodiment , the vfe modulates the wavefront of light such that an image from an operatively coupled display element ( such as a scanned light display , scanned laser display , dlp , lcd , lcos , oled , electrochromic display , electrowetting display , led array , or any other display technology known in the art ) is brought substantially into focus upon one of the switchable screens at a given time step . in one embodiment , the switchable screens are viewed directly by a viewer . in one embodiment , the switchable screen is operatively coupled a viewing optical system that relays light from the switchable screen to a viewer , such that image elements are perceived to be at an optical viewing distance . if the viewing optical system produces little or no field curvature , the image upon the switchable element will be relayed to form a substantially planar image to the viewer at the optical viewing distance . if the viewing optical system produces some detectable field curvature , the image upon the switchable element will be relayed to form a curved image to the viewer that subtends a range of optical viewing distances . for instance , the center of the image may be positioned at an optical viewing distance of 1 meter , while the periphery of the image may be positioned at an optical viewing distance of 1 . 1 meters . a rendering system operatively coupled to a display system that produces such a curved image plane to a viewer can adjust rendering characteristics of the displayed image elements as a function of their lateral position within the image . for instance , the rendering system can render objects intended to be at 1 meter in the center of the image , and render images intended to be at 1 . 1 meters in the periphery of the image . the rendering system can also render of simulated focus and depth of field for image elements as function of lateral position within the image . e . g ., in a 3d rendering system comprising a virtual camera , the focus of the virtual camera used to capture a projection of the 3d volume can be placed at 1 meter for image elements in the center of the image and at 1 . 1 meters for image elements near the edge of the image . if a plurality of switchable screens are stacked such they occupy different viewing distances from a viewer ( viewing the screens either directly or indirectly via an optical system ), then a plurality of image elements can be projected upon the plurality of switchable screens , such that light comprising different image elements reaches the viewer from different optical viewing distances . a viewer looking at the light field from the plurality of switchable screens can perceive a 3d volumetric image , with different objects at different focus levels and viewing distances . for instance , if the plurality of switchable screens comprises 10 layers of pdlc switchable diffusers , then a rendered ( and / or captured ) 3d scene can be sliced into 10 image slices , with each image slice being projected to a different pdlc screen . the different image slices may be projected by an operatively coupled display system to the stack of pdlc screens in a frame - sequential fashion , with the one pdlc layer being switched into a diffusive state and the other pdlc layers being switched into a transparent state at each time step , such that only one layer acts as a diffusing screen at a given time step . an operatively coupled vfe , such as a variable focus lens , can modulate the wavefront of light from the operatively coupled display element in a synchronous frame - sequential fashion , such that each slice of the rendered image is brought into focus on the pdlc layer that is switched into a diffusing state . the switchable screens can be used in a rear projection configuration and / or a front projection configuration . it can be a challenge to produce a vfe that simultaneously achieves a large effective aperture , large focus range , low power consumption , and high - speed focus modulation . the system described herein enables a relatively small vfe to be operatively coupled to a display source , as an operatively coupled stack of switchable screens increases the effective na of the relayed images to support a large eyebox , despite a small aperture in the vfe . in the art , it is known that it is non - trivial to design and fabricate an optical system to relay light from a display source without imparting some amount of field curvature . optical systems that are well corrected for field flatness are often larger , and more complicated and more costly to design and fabricate than an optical system that does not fully correct field curvature in relayed light . this disclosure also describes the use of a vfe to physically modulate the wavefront of incident light to perform field flattening or correction of field curvature . in one embodiment , the vfe is used to modulate the wavefront of light comprising image data that is incident upon the vfe , in order to perform field flattening to adjust an incoming light from a curved image field to form a substantially planar image field . in one embodiment , the light exiting the vfe is field flattened and brought substantially into focus upon a screen ( such as a switchable screen , as described herein , or such as a moving screen , or such as static screen ). in one embodiment , the vfe is operatively coupled to scanned light display ( such as a fiber scanned display , a scanning mirror display , a scanning laser display , flying spot display , or line scan display ) such that the vfe can modulate the wavefront of light differently at different scan positions . for instance , a fiber scanned display can be driven in a spiral pattern , such as a spot that starts in the center of the field and spirals outward to the edge of the field over time , with an operatively coupled light source modulated in synchrony with the scan pattern , to project imagery . a vfe that is operatively coupled to the fiber scanned display can change its optical power as a function of the eccentricity of the scanned spot , such that the center of a scanned image is focused with one optical power and the spots toward the edge of the image are focused with a different optical power . in this way , the curvature of the field can be adjusted dynamically on a pixel - by - pixel or line - by - line basis . this can enable an optical system with excellent field flatness in a very compact system ( e . g ., a single vfe instead of a stack of static lenses ). in addition to performing field flattening for an image projected to a screen at a given distance , the vfe can switch the overall focus of the image to a different screen in a plurality of switchable screens , as described herein . the vfe can correct the field curvature at each of the screen distances , to form a stack of substantially planar images comprising a 3d volume . the vfe works as the flattener and focusing lens . the vfe may comprise a small aperture size ( e . g ., 3 mm ), because it may be operatively coupled to a compact display source . the vfe may be driven with a continuously and smoothly varying signal , such as sinusoidal wave , to enable high frequency focus modulation while minimizing or eliminating ringing or other temporal artifacts . a 3d display system 100 as shown in fig1 can comprise a display unit 102 , vfe 104 , and viewing optics 106 . for such a configuration it is typically beneficial to use a vfe with a large aperture , to support a large eyebox or exit pupil for a viewer . however , typical large aperture vfes known in the art are not typically able to easily achieve fast response times , low operating voltage , compact size , low weight , and reliability for large aperture sizes . one embodiment is shown in fig2 . it comprises a fiber scanned display 202 ( hereinafter “ fsd ”) unit , a vfe 204 , stacked switchable diffusers 206 , and viewing optics 208 . the vfe 204 can be positioned close to the fsd 202 so that a small aperture size is sufficient to receive and relay the display light . the vfe 204 can focus the light from the fsd 202 to intermediate image planes aligned with a plurality of stacked switchable screens 206 , such as polymer - dispersed liquid crystal ( hereinafter “ pdlc ”) devices . at each time step , a single switchable screen is in a diffusing state while the other screens are in a substantially transparent state . the image projected upon on each switchable screen corresponds to a specific distance of a multi - focal image relayed to the viewer by the viewing optics . in addition to the field curvature that can be generated by simple conventional static lens designs , some embodiments of the fsd 202 comprise a curved image source . fig3 shows a simple optical model of the total field curvature 306 produced by a given fsd 202 and vfe 204 configuration , with the vfe in one static focus state . if left uncorrected , the field of curvature could poorly align with a flat projection screen , causing some pixels to be out of focus on the screen , while others are in focus . fig4 shows an example embodiment 400 of how one can vary the optical power ( in diopters ) of a vfe in coordination with a position of a scanned spot within the scan field . for instance , if the vfe is operatively coupled to a fsd scanning in a spiral pattern ( bottom left of fig4 ), the vfe can produce higher optical power for the light in the center of the scan and lower optical power for light at the periphery of the scan , smoothly varying as a function of eccentricity — yielding a substantially flat image field at the output . in one embodiment , the vfe is modulated in a substantially sinusoidal fashion to enable very high speed focus modulation . fig5 shows an example embodiment 500 of how the scan amplitude in an fsd spiral scan drive signal can be matched to the sinusoidal oscillation of the vfe to produce a flat field at the vfe output . the units in fig5 are derived from the exemplary vfe diopter to field position data in fig4 . in one embodiment , the vfe drive signal is adjusted away from a perfect sine wave to match a desired fsd scan amplitude pattern , while maintaining a substantially smoothed drive signal to the vfe to minimize ringing or other drive artifacts and support high speed focus modulation . fig6 illustrates an embodiment 600 t that generates four depth planes ( i . e ., fixation distances ) ( 602 , 604 , 606 and 608 ) in a time sequential fashion . in this embodiment , the vfe is driven with a sinusoidal wave swinging through a total focus range of 36 . 80 diopters ( 1 / m ) to 49 . 58 diopters . the amplitude of the peaks and troughs of the sinusoidal wave are adjusted on a time sequential basis in synchrony with the projection of image slices by the scanned light display ( e . g ., fsd ), such that the focus of each of the 4 image slices is swept through a different subset of the total focus range . the overall offset between the focal range subsets corresponds to different optical viewing distances of the image slices presented to a viewer . the variation within each image slice &# 39 ; s focus range enables the center of the image to be focused with a different optical power than the periphery , correcting field curvature and producing a substantially flat image field for each depth plane . as an example , fsd scanning angles between − 20 ° and 20 ° are depicted . the vfe diopter range in fig6 is consistent with the exemplary vfe diopter to field position data in fig4 . fig7 shows one variation 700 of a drive signal to the vfe that is not sinusoidal . in this case , a triangular wave ( open squares in the figure ) is used to drive the vfe focus state . fig7 also shows how the scan amplitude in an fsd spiral scan drive signal ( dark circles in fig7 ) can be matched to the oscillation of the vfe to produce a flat field at the vfe output . the units in fig7 are consistent with the exemplary vfe diopter to field position data in fig4 . the dynamic field flattening method and system using a vfe and the multi - focal display system comprising a plurality of switchable screens can be utilized in isolation from one another , or they can be employed in a shared system to good effect . various exemplary embodiments of the invention are described herein . reference is made to these examples in a non - limiting sense . they are provided to illustrate more broadly applicable aspects of the invention . various changes may be made to the invention described and equivalents may be substituted without departing from the true spirit and scope of the invention . in addition , many modifications may be made to adapt a particular situation , material , composition of matter , process , process act ( s ) or step ( s ) to the objective ( s ), spirit or scope of the present invention . further , as will be appreciated by those with skill in the art that each of the individual variations described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present inventions . all such modifications are intended to be within the scope of claims associated with this disclosure . the invention includes methods that may be performed using the subject devices . the methods may comprise the act of providing such a suitable device . such provision may be performed by the end user . in other words , the “ providing ” act merely requires the end user obtain , access , approach , position , set - up , activate , power - up or otherwise act to provide the requisite device in the subject method . methods recited herein may be carried out in any order of the recited events which is logically possible , as well as in the recited order of events . exemplary aspects of the invention , together with details regarding material selection and manufacture have been set forth above . as for other details of the present invention , these may be appreciated in connection with the above - referenced patents and publications as well as generally known or appreciated by those with skill in the art . the same may hold true with respect to method - based aspects of the invention in terms of additional acts as commonly or logically employed . in addition , though the invention has been described in reference to several examples optionally incorporating various features , the invention is not to be limited to that which is described or indicated as contemplated with respect to each variation of the invention . various changes may be made to the invention described and equivalents ( whether recited herein or not included for the sake of some brevity ) may be substituted without departing from the true spirit and scope of the invention . in addition , where a range of values is provided , it is understood that every intervening value , between the upper and lower limit of that range and any other stated or intervening value in that stated range , is encompassed within the invention . also , it is contemplated that any optional feature of the inventive variations described may be set forth and claimed independently , or in combination with any one or more of the features described herein . reference to a singular item , includes the possibility that there are plural of the same items present . more specifically , as used herein and in claims associated hereto , the singular forms “ a ,” “ an ,” “ said ,” and “ the ” include plural referents unless the specifically stated otherwise . in other words , use of the articles allow for “ at least one ” of the subject item in the description above as well as claims associated with this disclosure . it is further noted that such claims may be drafted to exclude any optional element . as such , this statement is intended to serve as antecedent basis for use of such exclusive terminology as “ solely ,” “ only ” and the like in connection with the recitation of claim elements , or use of a “ negative ” limitation . without the use of such exclusive terminology , the term “ comprising ” in claims associated with this disclosure shall allow for the inclusion of any additional element -- irrespective of whether a given number of elements are enumerated in such claims , or the addition of a feature could be regarded as transforming the nature of an element set forth in such claims . except as specifically defined herein , all technical and scientific terms used herein are to be given as broad a commonly understood meaning as possible while maintaining claim validity . the breadth of the present invention is not to be limited to the examples provided and / or the subject specification , but rather only by the scope of claim language associated with this disclosure .