Optical performance requirements for MEMS-scanner based microdisplays

Transcription

1 Optical performance requirements for MEMS-scanner based microdisplays Hakan Urey, Daid W. Wine, Tor D. Osborn Microision Inc., Nort Creek Pkwy, Botell, WA Pone/Fax: +1(425) / 6601, HakanU@mis.com ABSTRACT Hig-resolution (i.e., large pixel-count) and ig frame rate dynamic microdisplays can be implemented by scanning a poton beam in a raster format across te iewer s retina. Microision is deeloping biaxial MEMS scanners for suc ideo display applications. Tis paper discusses te optical performance requirements for scanning display systems. Te display resolution directly translates into a scan-angle-mirror-size product (θd-product) and te frame rate translates into ertical and orizontal scanner frequencies (f and f ). θd-product and f are bot ery important figures of merit for scanner performance comparison. In addition, te static and dynamic flatness of te scanners, off-axis motion and scan repeatability, scanner position sensor accuracy all ae a direct impact on display image quality. eywords: Scanner, Resolution, Retinal Scanning Display, RSD 1. INTRODUCTION Tere are many competing tecnologies for displays tat are used in and-eld or ead-worn deices. Microision is deeloping te Retinal Scanning Display (RSD) tecnology, were point ligt sources (e.g., laser diode, fiber-coupled laser, LED) are scanned onto a screen or directly onto a retina as a 2-D raster pattern using two uniaxial or one biaxial scanner. Current Microision RSDs use torsional flexure-based mecanical scanners tat ae te potential to enable a scanning display tat meets te simultaneous requirements of speed, resolution, size, and cost, wile retaining all oter adantages demonstrated by oter scanning systems (e.g., laser printer, CRT) 1. For example, te single scanned pixel can be well controlled witout many of te compromises needed to treat 10 6 pixels of a matrix display. Microision as deeloped an array of scanning tecnologies tat sow promise for RSDs, including Microision s mecanical resonant scanner and biaxial MEMS scanners. Anoter paper publised in tese proceedings discusses te scanner and display performance using current Microision MEMS scanners. 2 For mass production at low cost, MEMS scanners ae significant adantages compared to matrix displays, including smaller wafer area and iger yield, especially for VGA and iger resolutions. Furter deelopment of compact ligt sources and MEMS scanner tecnology will assist RSD tecnology in growing rapidly in a number of dierse application areas. In tis paper we reiew te scanner performance requirements for scanner based dynamic display systems using mecanical scan mirrors. Section 2 discusses biaxial scanner arcitecture and RSD operation. Section 3 details te resolution, pixel timing, scanner frequency, and raster quality requirements. Section 4 discusses dynamic flatness teory and presents results of MEMS scanner dynamic flatness measurements. 2. SCANNER ARCHITECTURE AND RSD OPERATION In tis paper we assume tat te orizontal scan axis is resonant, and te ertical scan axis is non-resonant and drien wit a sawtoot waeform at te refres rate of te display. As will be discussed in Section 3.2, te orizontal scanner will typically run at frequencies exceeding 10 Hz, and sould proide a large scan angle-mirror size product. Te resonant torsional scanner can meet tese frequency and resolution requirements wit te added adantage of low power consumption. Additionally, te resonant orizontal scanner can proide a master pixel clock for te system. For good image quality, te ertical scan position and frequency sould derie from te orizontal scanner position and frequency. Terefore, te ertical axis is preferably non-resonant and drien wit a waeform tat proides equal spacing between raster lines. A fast ertical retrace time at te end of eac frame reduces constraints on te system design caused by limited frame periods. 1

2 A 2-D raster can be generated using one biaxial or two uniaxial scanners. Uniaxial scanners are simpler to design and fabricate; oweer, biaxial scanners proide important optical and packaging adantages for display systems. Te analysis in tis paper is generally applicable to bot types of scanners. Figure 1 sows a scematic of a Microision MEMS scanner. Te biaxial scanner arcitecture eliminates te need for a second scanner and makes te system muc more compact. Te orizontal scan mirror is supported wit two torsional flexures and operates in resonant mode. It as a ig Q-factor, tus it requires small amount of power to operate in closed loop. Te ertical axis is drien non-resonantly in a sawtoot pattern at te desired display frame rate. Te orizontal axis is actuated electrostatically and te ertical axis is actuated magnetically. Horizontal Scan mirror Vertical scan frame and drie coils Figure 1: Diagrammatic iew of Microision MEMS scanner Figure 2 depicts te cross-section of te optical pat for te ead-worn unit of an RSD using a biaxial scanner. Te ligt source can be a directly modulated source suc as a laser diode or LEDs, or an externally modulated source, suc as red, green, and blue lasers tat are coupled to a single mode fiber. Te biaxial scanner draws a 2-D raster across te intermediate image plane. For laser-based RSDs, te lasers, modulators, and color combining optics are typically located remotely, allowing for ligt-weigt ead mounted unit. Optics for te RSD includes an intermediate image plane between te scanner and te exit pupil of te display and typically produces a small exit pupil. Tis limitation can be traced to te optical inariant or te Lagrange inariant and can be remoed using an exit pupil expander (EPE) at te intermediate image plane. 1 Te EPE is essentially a forward-scattering diffuser screen tat increases te exit pupil size from te typical 1-2mm to 15mm or larger. Te EPE is implemented using a periodic 2-D diffraction grating tat creates replicas of te 1-2mm pupil across a muc larger exit pupil. Te large exit pupil allows te user s eye and ead to moe relatie to te display oer a large range witout losing te image. For flat panel tecnologies, te microdisplay panel is located at te EPE plane and te iewing optics or ocular is about te same for all tecnologies. Depending on te MTF and field-of-iew requirements, te ocular can be a simple eyepiece or a multi-element lens system. Te image information is contained witin te total ideo scan angle (TVSA) sown in te figure. 2

3 Bi-axial Scanner D Fiber or oter ligt source TVSA Intermediate Image Plane Ocular (iewing optics) D lens θ o FOV Exit pupil Viewer s eye θ i Exit Pupil Expander Figure 2: Cross-sectional iew of te optical pat for Retinal Scanning Displays 3. SCANNER REQUIREMENTS For scanners, te igest resolable spatial frequency is determined by te scan angle required to moe te tip of te scan mirror by approximately λ/2. Τe motion of te tip of te scanner is proportional to te product of te scan angle and te mirror size. Tus, te total number of resolable spots for te scanner is proportional to te scan angle mirror size product (θd-product) for te scanner and inersely proportional to te ligt waelengt. Likewise, in scanning displays, display resolution requirement directly translates into a θd requirement and te display refres rate requirement translates into ertical and orizontal scanner frequencies (f and f ). Bot te θd-product and f are ery important figures of merit for scanner performance comparison. In calculating te required θd-product for a gien display format, one as to factor in (1) beam profile across te scanner (e.g., clipping ratio of Gaussian beams) and operation waelengt; (2) usable portion of te scan line (limitations due to sinusoidal motion of resonant scanners); (3) clear aperture size of te scanner; (4) display MTF and contrast requirements; and (5) static and dynamic flatness of te scan mirror surface. Oter important requirements are related to scan repeatability and accuracy of scanner position information from position sensors. All of tese parameters ae a direct impact on display image quality and are discussed in tis section and Section 4. Luminance requirements of displays are not discussed in tis paper Resolution and Number of Pixels As discussed aboe, te resolution of te scanner is proportional to te θd product of te scanner. Besides te number of pixels, many oter factors impact te θd requirements for te scanner. For instance, one important adantage of laser scanning systems is tat one scanner can be used to redirect multiple beams simultaneously, tereby improing te orizontal or ertical resolution of te display. As an example, four-beam unidirectional scanning as been successfully implemented at Microision. In te four-beam approac, eac feed beam is coupled to a different ligt source modulator and all beams are combined togeter in a four-cannel waeguide. Multiline writing increases te line rate of te system by te number of beams. Wen a multi-beam approac is considered te general scan equation for orizontal and ertical resolution of a scanning display system can be written as: N 4 θ MMSAD sp os _ aλ T cos( α) = (1) 3

4 N 4 θ MMSA D sp os _ aλ T ub cos( α) n = (2) f s r = (3) ub F N os _ n N = orizontal resolution of display N = ertical resolution of display D = scan mirror size along orizontal axes D = scan mirror size along ertical axes θ MMSA = Maximum mecanical scan angle amplitude (0-peak) θ MMSA = Maximum mecanical scan angle amplitude in ertical axes (0-peak) θ TVSA = Total ideo scan angle (θ TVSA = 4θ MMSA os ) sp = spot size to pixel size ratio (typically 0.5<sp<2) os ( os_ and os_ ) = oerscan constants ( os ÃÃIRUÃRUL]RQWDOÃDQGÃYHUWLFDOÃD[HV ub = 1 for unidirectional and 2 for bidirectional scanning α= feed beam angle (can be different for orizontal and ertical axis) n = number of ertical feed beams T = beam clipping constant a = mirror sape factor (a =1 for square/rectangular mirrors) f s = orizontal scanner frequency (Hz) F r = frame rate or refres rate for te display (typically 60Hz) f = ertical scanner frequency (f = F r ) Spot Oerlap ( sp ): sp is te ratio of te spot size to pixel size and is a ery important parameter in scanning display design. Because te orizontal scanner is a continuous motion deice, te display as effectiely infinite addressability in te orizontal direction. Te amount of spot oerlap between adjacent pixels is te main parameter tat determines te MTF of te display. 3 Pixel size is typically cosen equal to full-widt at 50% irradiance of te Gaussian spot (FWHM). Tis corresponds to a sp of 1.0. Tis ratio determines raster modulation (RM) and contrast ratio (CR). Raster modulation is an undesired background modulation effect tat can be obsered in areas were te beam is ON during eery sweep. For sp =1, RM and CR are about 6% and 78%. In some applications, 6% RM is objectionable and can be reduced at te expense of contrast by increasing sp. Oerscan Factor ( os ): Te speed ariations resulting from sinusoidal motion of resonant scanners produces pixel size and brigtness ariations across te scan line. Typically, writing is alted during te extremities of te scan line to minimize te speed ariation. Te pixel size and brigtness ariations during te isible portion of te scan can be easily corrected electronically. In te aboe calculation, te orizontal oerscan factor, os_, accounts for te unused portion of te scan, and usually ranges from 0.7 to 0.9. Similarly, te ertical oerscan factor, os_, takes into account te retrace time of te nonresonant ertical scanner and usually ranges from 0.9 to Beam Clipping ( T ): Te diffraction limited spot diameter for a clipped Gaussian beam is proportional to focal-ratio (f # ) of te focusing geometry, waelengt of te ligt, and beam clipping constant T, wic is a function of te amount of beam clipping at te limiting system aperture (scanner in tis case). Te spot diameter is: s FWHM = T, FWHM λf # (4) were te FWHM spot size for clipped Gaussians can be calculated using te following formulas: , T 0.4( Clipped Gaussian) 2 T T T FWHM > = (5) 4

5 0.75, T 0.5 ( Gaussian) T T FWHM < = (6) Te truncation ratio, T, is te ratio of feed beam 1/e 2 diameter (FWE2) at te mirror to te mirror diameter. Equation 5 is found by cure-fitting to te Huygens-Fresnel diffraction integral for clipped Gaussian beams. Note tat T can be different for te orizontal and te ertical axes. Gaussian beam formulas are alid for T<0.5 (i.e., beam clipping is negligible). Various alues of T are sown in te Table below. Table 1: Beam Truncation ratio and te corresponding spot size proportionality factor for Gaussian beams. Truncation Ratio Scanned Beam Sape T, FWHM Value T = 0.5 Full Gaussian (clipping negligible) 1.5 T = 1 Gaussian truncated at FWE T = 2 Uniform center (87%) of Gaussian 1.05 T Uniform beam (focused spot is Airy pattern) 1.04 Feed Beam Angle, cos(α): Te angle of te incoming beam also affects pixel size resolution. As te incoming beam angle α increases from ertical (α = 0), te projected area of te spot on te mirror increases as a cosine function, wic must be taken into account. α can be different for te orizontal and te ertical axes. Unidirectional/Bidirectional and Multibeam Scanning ( ub, n ): Bidirectional scanning refers to writing or displaying a new line of data in bot scan directions as opposed to writing data only during te forward sweep of te orizontal scanner. Tis is discussed in more detail in Section 3.3. Bidirectional scanning doubles te display line-rate by permitting te scanner to write two lines during one scan cycle. Using multiple beams to scan multiple lines furter increases te ertical resolution by increasing te number of lines written during a single sweep of te scan mirror. As illustrated by Equation 3, orizontal scanner frequency is inersely proportional to te number of scan beams. Te number of beams, N, in a gien display will depend on a ariety of factors, suc as te complexity of te oerall system, cost, and optical alignment considerations. Table 2 sows te θd requirements for ig-performance RSDs. Te assumptions on os, T, λ, and θ inc for eac display format are te same. sp for all display formats are 1.0 (i.e, FWHM spot size equal to display pixel size). Te only exception is te column labeled SVGA2, wic as a sp of 1.5. SVGA2 case requires 2/3 of te θd-product of te SVGA1 case. Wile bot of tem can display SVGA ideo, te SVGA1 display produces a better MTF, better contrast modulation, and sarper edges compared to te SVGA2 display. Once te θd-product is determined, te coice of θ and D sould be based on dynamic mirror flatness, maximum allowable optical scan angle due to optical constraints and te mecanical stress limitations on te flexures, drie circuit requirements, and cost (parts per wafer). 5 Table 2: θd requirements for different display formats for ig-performance RSDs. Units QVGA VGA SVGA_1 SVGA_2 XGA SXGA UXGA HDTV Number of orizontal pixels N Fraction of scan line used for writing os Spotsize (FWHM) to display pixel size ratio sp Truncation ratio (Gauss beam diam./mirror diam.) T Waelengt λ um Incidence angle θ inc deg Spot size constant for FWHM (function of T) FWHM peak mecanical scan angle * mirror size product θ MMSA D deg.mm

6 3.2. Frequency and Pixel Timing Requirements Te resonant orizontal scanner moes fastest at te center of te scan and comes to a stop at te extremities of te scan. os, discussed in Section 3.1, defines te usable portion of te scan line. Witin te usable area, pixel time sould be aried electronically to produce display pixels wit equal widt. Te pixel time at te center (t c ) and te edges (t e ) of te display can be expressed as: t c πf os _ =, (7) N Te maximum allowable ertical retrace time t ret can be expressed as t 1 2 e = os _ os _, πf N (8) t 1 N f (1 f 2 f ret = ) (9) Figure 3 sows te required ertical retrace time as a function of orizontal scanner frequency for VGA and SVGA bidirectional scanning display systems. Te orizontal frequency requirement for SVGA display is 20% iger tan VGA display. Reducing te retrace time allows for smaller orizontal frequency and longer pixel times. Horizontal Scanner Frequency Requirements for 60Hz Refres Rate Bi-Directional Scanning Display Frequency (Hz) Vertical Retrace Time (msec) VGA SVGA Figure 3: Vertical retrace time and orizontal frequency requirements for scanning displays. Table 3 sows te pixel time, ertical retrace time, and frequency requirements for different display formats and system arcitectures. Note tat, wen 90% of te total scan angle is used for ideo display, pixel time aries by a factor of 2.3 from center to te edge. Also note tat, te pixel time reduces wit increasing display resolution, requiring faster modulators. 6

7 Table 3: Pixel timing and frequency requirements for arious display formats and display arcitectures Display Format VGA SVGA XGA SXGA HDTV Fr - Frame Rate (progressie) (Hz) N - Horizontal Scan Pixel Number N - Vertical Scan Pixel Number (Number of Lines) f - Horizontal Scanner Frequency (Hz) os - Fraction of te scan-line lengt used for writing n - Number of parallel scan lines for uni-directional & 2 for bi-directional scanning tret - Maximum retrace time allowed for ertical scanner (msec) Pixel-time at te center of orizontal scan line (nsec) Pixel-time at te edge of te written area (nsec) Maximum pixel clock frequency (MHz) Raster Quality Figure 4 illustrates considerations of unidirectional and bidirectional scanning and certain adantages and disadantages of eac. Bidirectional scanning increases te ligt source utilization by a factor of 2 and reduces te required orizontal scanner frequency by a factor of 2. Howeer, it requires buffering one line of data and displaying it in reerse order during backward sweep of orizontal scanner, requires precise control of te pase between forward scan and backward scan lines, and can produce non-uniform line-to-line spacing across te scan line. Figure 5 sow simulation results for te isual effect of nonuniform line spacing for bidirectional scanning arcitecture. Te strong correlation between te simulation and actual systems can be seen by comparing te simulated results of Figure 4 to te actual ideo display system results described in Ref. 2. Te text in te simulation is 10pt font placed at te center and at te edge of te display. Te non-uniform line spacing results in brigtness ariations and somewat reduces te contrast modulation for points away from te center of te screen. Te amount of usable screen widt for te bidirectional scanning sould be determined based on te display image quality requirements. Unidirectional Scanning Bidirectional Scanning TVSA center edge Figure 4: 2-D raster for unidirectional and bidirectional scanning. 7

8 Bidirectional Scanning Simulated resultant image patterns Center of screen Edge of screen Figure 5: Simulated resultant display image at te center and te edge of te screen for te bidirectional scanning arcitecture sown in Figure 4. Text is 10pt Arial. sp is 1.0 in te orizontal axes and 1.2 in te ertical axes. Te motional blur in te orizontal axis for a 100% pixel-duty-cycle is also taken into account (i.e. ligt is turned on at te beginning of te pixel time and kept on during te entire pixel time) Oter Requirements Seeral oter factors can affect te image quality. For instance, te non-linearity of te ertical scan sould be less tan 0.1% across te ertical scan line. Te orizontal scanner position and te frequency need to be determined ery accurately and as to be monitored continuously. Line-to-line jitter and frame-to-frame jitter depend on ow accurately te scan position and te frequency can be syncronized wit te data clock and te ertical scanner. Te total jitter in te system sould be at subpixel leels. If we assume a maximum of 1/8 pixel off-axis motion for te orizontal scanner, te jitter in te system including electronics, position sensor, and mecanical scanner sould not exceed 3-4 nsec at 1σ. Optical and mecanical design of te scanner ousing imposes additional constraints in scanner design. Manufacturing and alignment tolerances become ery tigt for small scan mirrors. Small mirrors require large scan angles, and large scan angles result in focus errors and a non-flat image plane (i.e., field curature). Field curature can be corrected optically, but for low cost and low weigt ead-mounted display applications, tere is no room for field correction lenses. All tis imposes a lower bound on te scanning mirror size STATIC AND DYNAMIC MIRROR FLATNESS Bot te static and te dynamic flatness of te scan mirror are important for image quality. As illustrated in Figure 6(a), ig acceleration forces during mecanical deflection of te mirror result in bending of te mirror. Een ery small amount of deiation from linearity due to mecanical deformation can result in optical distortion of te pixel and te image. Maximum deformation occurs at te extremities of te scan. For rectangular block mirrors, te following formulas 6,7 can be used to compute mirror deformation, wic is defined as te deiation from linearity as sown in Figure 6(a): δ ( u) = δ ( u 10u + 20u 11u )/1.83 (10) max D δ = (11) 2 5 ρf θ MMSA max Etm u = normalized mirror surface coordinate perpendicular to rotation axis ρ = material density E = modulus of elasticity (Young s modulus) f = scanner frequency 8

9 Normalized Deformation 1 D t m 0.5 MMSA MMSA/2 Rotation axis D/2-0.5 θ MMSA δ max T -1 Normalized scan mirror coordinate Figure 6: (a) Dynamic mirror deformation grapical representation, (b) surface profile as a result of deformation. Maximum deiation from linearity attained at about 40% of te way from center to te edge of te scanner. Figure 6(b) sows te sape te mirror surface takes as a function of u (u = ±1 corresponds to te edges of te mirror). As seen from te figure, te deformation is symmetrical wit respect to te center of te mirror. For te kind of aberration te mirror introduces, te maximum mecanical mirror deformation (δ max ) sould not exceed λ/10 (λ/5 optical pat difference) of te sortest system waelengt. Tis will permit te spot to remain diffraction limited across te scan line. Note tat δ max is proportional to D 5 θ. Due to ig sensitiity to canges in D, if te system performance is deformation limited, significant gains can be attained by sligtly reducing te mirror size. Brosen s formulas 6 predict dynamic deformation only along te scan axis. Microision as deeloped and built a stroboscopic interferometer to measure te dynamic flatness of scan mirrors and to test te alidity of te teory. Results to date indicate tat te one-dimensional teoretical formulas ae limited accuracy. Te experimental results and dynamic deformation calculations will be reported in detail in a future publication. Figure 7 sows te experimental results for dynamic flatness of a biaxial MEMS scanner. Te scanner frequency was about 18Hz and mirror was 1.2mm square. Te surface flatness in units of OPD was measured to be better tan λ/10 bot at te center of te scan and at te edge of te scan (+3.75 mecanical scan angle). Tus, te mirror sould produce a diffraction-limited spot across te entire scan line. Aside from te measurement errors, te only notable difference between te center and te edge interferograms is te bending of te mirror at flexure joints. 5. SUMMARY AND CONCLUSIONS Mecanical scanners based on MEMS tecnology can be used in dynamic display applications and can proide important performance and fabrication adantages compared to oter display tecnologies. As discussed trougout tis paper, igperformance displays impose ery stringent requirements on te scanners. Tree most important figures of merit for scanner ealuation can be stated as scan angle-mirror size product (θd-product), scanner frequency, and dynamic surface flatness. Tis paper as defined te necessary deelopment pat for biaxial scanning tecnology to satisfy te requirements of display applications. Microision scanners ae demonstrated performance at te SVGA1 and SVGA2 leel (see Table 2) in te laboratory altoug certain engineering obstacles must be oercome to meet tis performance in production. 2 We beliee tat all te performance leels discussed aboe are approacable wit furter deelopment of our MEMS scanning tecnology ACNOWLEDGMENTS We tank arlton Powell for elp wit some of te simulations, and Abraam Gross and Jon Lewis for elpful discussions. 9

10 Experimental Dynamic Flatness Test Results for 1.2mm Biaxial MEMS Scanner Dynamic Flatness (at 0 deg scan angle) OPD in waes (at 635nm) y-axis(mm) x-axis(mm) Dynamic Flatness (at deg mecanical scan angle) OPD in waes (at 635nm) y-axis(mm) x-axis(mm) Figure 7 (a) Stroboscopic interferogram of te scanner at 0deg scan position wen te mecanical scan amplitude was 3.75deg, (b) corresponding optical pat difference (OPD is equal to twice te mecanical flatness of te mirror). (c) Interferogram of te scanner at te maximum scan angle, (d) corresponding optical pat difference. REFERENCES 1. H. Urey, Optical Adantages of Retinal Scanning Displays, Helmet and Head-Mounted Displays V, Proc. SPIE Vol. 4021, pp , Orlando, Florida, April D. W. Wine, M. P. Helsel, L. Jenkins, H. Urey, T. D. Osborn, Performance of a Biaxial MEMS-Based Scanner for Microdisplay Applications, Conf. on MOEMS and Miniaturized Systems, Proc. SPIE Vol. 4178, Santa Clara, California (2000) 3. H. Urey, N. Nestoroic, B. Ng, A. Gross, Optics designs and system MTF for laser scanning displays, Helmet and Head-Mounted Displays IV, Proc. SPIE Vol. 3689, pp , Orlando, Florida, Marc H. Urey, Spot size and dept-of-focus formulas for clipped Gaussian beams in preparation. 5. H. Urey, D. W. Wine, J. R. Lewis, Scanner design and resolution tradeoffs for miniature scanning displays, Flat Panel Display Tecnology and Display Metrology, Proc. SPIE Vol. 3636, pp , San Jose, California, January P. J. Brosens, Dynamic mirror distortions in optical scanning, Applied Optics, ol. 11, pp , D. Dickenseets, A microfabricated scanning confocal optical microscope for in situ imaging, P.D. Tesis, Stanford Uniersity, Stanford,