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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 12 — Apr. 20, 2013
  • pp: 2610–2618
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Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators

Stephan Reichelt  »View Author Affiliations


Applied Optics, Vol. 52, Issue 12, pp. 2610-2618 (2013)
http://dx.doi.org/10.1364/AO.52.002610


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Abstract

Methods for measuring and compensating the nonlinear electro-optical effect of transmissive, parallel-aligned liquid crystal (LC)-based spatial light modulators (SLMs) are presented. Particularly, the analysis is focused on the spatial nonuniformity of the voltage versus phase modulation characteristics for an active-matrix-driven, electrically controlled birefringence type LC-SLM. A high-quality reconstruction from phase-only modulating SLMs requires a well-calibrated phase addressing across the entire SLM panel. I discuss how the commonly inherent phase-response inhomogeneity of LC-SLM is characterized by purposeful localized measurement techniques. This phase-response inhomogeneity is efficiently compensated by utilizing a Legendre polynomial representation in combination with a remapping of an 8 bit gray level addressing. The calibration procedure is corroborated by measurement data. The LC-SLM’s experimental demonstration finally verifies the resultant improvement in holographic imaging.

© 2013 Optical Society of America

1. Introduction

Accurate phase calibration is essential for liquid-crystal-based spatial light modulators (LC-SLMs) in their use as programmable diffractive devices. Several calibration methods for both reflective and transmissive SLMs have been reported and compared [1

1. C. Kohler, X. Schwab, and W. Osten, “Optimally tuned spatial light modulators for digital holography,” Appl. Opt. 45, 960–967 (2006). [CrossRef]

3

3. A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007). [CrossRef]

], where the main focus of interest was on small-sized transmissive LC-SLM [4

4. A. Bergeron, J. Gauvin, F. Gagnon, D. Gingras, H. H. Arsenault, and M. Doucet, “Phase calibration and applications of a liquid-crystal spatial light modulator,” Appl. Opt. 34, 5133–5139 (1995). [CrossRef]

,5

5. K. Dev, V. R. Singh, and A. Asundi, “Full-field phase modulation characterization of liquid-crystal spatial light modulator using digital holography,” Appl. Opt. 50, 1593–1600 (2011). [CrossRef]

] as used in former video projectors and on reflective liquid-crystal-on-silicon (LCoS) displays [6

6. J. W. Tay, M. A. Taylor, and W. P. Bowen, “Sagnac-interferometer-based characterization of spatial light modulators,” Appl. Opt. 48, 2236–2242 (2009). [CrossRef]

8

8. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51, 3837–3846 (2012). [CrossRef]

].

Basically three effects might deteriorate the overall SLM performance with regard to its phase-representing capability: (1) a global static phase error (or wavefront aberration) ϕ(x,y) caused by surface figure errors of the SLM substrates or cell-gap inhomogeneities; (2) a nonlinear dynamic phase response, that is, a phase retardation that depends on the address voltage ϕ(V) and its polarity; and (3) temporal fluctuations [7

7. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Dynamic calibration for improving the speed of a parallel-aligned liquid-crystal-on-silicon display,” Appl. Opt. 48, 4616–4624 (2009). [CrossRef]

,9

9. A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16, 722 (2008).

] of the phase modulation ϕ(t) caused by the LC response time itself or the addressing method and driving scheme, respectively. Note there are interdependencies of all three contributions—as, for example, a cell-gap thickness variation will not only result in a global static phase error but also in a spatially nonuniform phase response. Or, the display architecture, driving scheme, and response time determine the time within a frame where the phase is best represented at every pixel of the SLM. Moreover, the resultant phase retardation of a single pixel might be affected by the spatial frequency of the addressed phase distribution, especially for a small LCoS-sized pixel where fringe fields and thus pixel cross talk cannot be neglected anymore [3

3. A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal-based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007). [CrossRef]

].

The phase calibration procedure detailed in the remainder of this paper utilizes a dedicated, active-matrix-driven 2π-phase electrically controlled birefringence (ECB)-mode transmissive LC-SLM, which operates in frame inversion at 60 Hz. The LC-SLM has mobile display size, a video graphics array (VGA) resolution comprising a rectangular pixel with a native pitch of px=84μm and py=28μm. This work is confined to the calibration of the spatially nonuniform, nonlinear dynamic phase response ϕ(V,x,y) for the following reasons. First, the LC-SLM under study is a transmissive-type LC-SLM for which the full-aperture global phase error is negligibly small for the intended application in holographic imaging. In the off state, the observed single-pass wavefront error was 720 nm peak to valley with a 95 nm rms over the full aperture (measured in double pass by a Twyman–Green interferometer at λ=632.8nm). Second, temporal phase fluctuations due to LC response and scanned active-matrix addressing are decreased to a large extent by synchronizing a pulsed laser light illumination with the SLM frame rate, which is timed to the end of the frame with a 20% duty cycle. Third, the active-matrix LC-SLM is intentionally driven in frame inversion mode to prevent a phase averaging during the phase-response measurement that otherwise could occur for a pattern-based polarity inversion scheme with inherently asymmetric gamma curves for positive and negative driving voltages. Measurement and subsequent usage of the LC-SLM has always been done within the frame of same voltage polarity (odd or even frame only, i.e., with half of the frame rate) with a pulsed monochrome (λ=532nm) laser illumination. Without loss of generality, it should be evident that the method presented below can be applied to the frame or pixel area with inverse voltage polarity and to other wavelengths in the same way.

This paper starts with a brief recapitulation of the electro-optical operation of ECB-mode LC-SLMs. I then provide methods for local measurement of the nonlinear phase response, present means for efficient data interpolation, and discuss how to compensate for the local varying phase-response characteristics. After an experimental verification of the resultant improvements, I end with some concluding remarks.

2. Electro-Optical Operation of ECB-Mode LC-SLM

The ECB mode is an LC switching mode often used in display applications. Figure 1 shows the schematic layout of an ECB cell, which uses a nematic LC that is homogeneously parallel aligned to the surfaces when no electrical field is present. In the off state, the ECB cell has the effect of an a plate of uniaxial material. When voltage is applied to the electrode, the electrical field in the z direction, perpendicular to the LC director, causes a tilt of the LC molecules and thus a change in the birefringence of the cell. The voltage-dependent retardation Γ of the ECB cell can be expressed as
Γ=k0d[ne(θ)no]dz=kd(neffno),
(1)
where k=2π/λ is the wavenumber, d is the thickness of the LC layer, θ is the tilt angle of the LC director, neff is the effective refractive index, and ne, no are the principal refractive indices of the LC material [15

15. P. Yeh and C. Gu, Optics of Liquid Crystal Displays, 2nd ed. (Wiley, 2010).

].

Fig. 1. Schematic drawing of an ECB cell in off and on states. The LC director is rotated to the tilt angle θ when an electric field is applied. Light propagation is in the positive z direction.

Assuming completely polarized light and idealized components (no absorption or reflection), the optical characteristics of the birefringent, variable retarder (ECB cell) can be described by Jones calculus. The Jones matrix for an ECB cell with parallel alignment of the LC molecules can be written as
JECB=(100eiϕy(V))
(2)
with ϕy=Γ being the voltage-dependent phase shift due to the birefringence Δn(θ)=neff(θ)no when the LC molecules are reoriented to the polar angle θ(V). Note that in an ECB cell, the retardation is maximum for zero voltage, that is, the voltage-dependent relative phase shift is ϕ(V)<0.

An ECB cell or an LC-SLM comprising an array of ECB pixels normally features a sigmoid electro-optical phase response to the applied voltage. After a certain threshold voltage Vth, the phase shift steadily increases, runs through an inflection point, and then slowly approaches a maximum value. To achieve a relative phase shift over the entire range from 0 to 2π for all wavelengths, the LC’s birefringence Δn and the cell thickness d must be designed such that it matches the longest wavelength. In this context, however, the effective addressing bit depth for other wavelengths than the longest wavelength must be reconsidered. If, for example, the ECB-LCD is designed for red light and 8 bit addressing, for blue light, the effective addressing bit depth is reduced by a factor that corresponds to the ratio of phase at the shortest and longest wavelength (e.g., with a red 8 bit gray-level bitmap addressing over the 2π range, for blue light only approximately 190 gray levels, and thus phase levels remain). It is therefore desirable to provide a certain reserve in the bit depth when a gray-level bitmap addressing is used for several colors.

A. Amplitude Modulation

To convert the phase shift into amplitude modulation, the ECB-mode LC-SLM has to be placed between crossed polarizers oriented at ±45°. The Jones matrix for amplitude modulation of such a device is then
JAM=JL45P·JECB·JL+45P=12(1111)(100eiϕy(V))12(1111).
(3)

When illuminated with linear polarized light at 45°, the output Jones vector is Eout=JAMEin with Ein=1/2[1;1]. The resulting intensity at the output is I(V)=Eout·Eout. That is, according to the phase response ϕy(V), the output intensity varies between the limits of 0 and 1, whereas the phase difference between x and y component remains constant.

B. Phase Modulation

No additional polarizing components are required for phase modulation of the ECB-mode LC-SLM. The Jones matrix for pure phase modulation is simply
JPM=JECB=(100eiϕy(V)).
(4)

When illuminated with linear vertically polarized light, the output Jones vector is then Eout=JPMEin with Ein=[0;1]. This is a pure y-component phase modulation of unity intensity.

3. Local Measurement of the Nonlinear Phase Response

In the following, methods for local characterization of the phase response of ECB mode LC-SLMs are discussed. Remember that the methods apply solely to phase-only modulating LC-SLMs where no geometric phase is involved. I will differentiate here between indirect methods for which the phase response is derived from intensity measurements with the help of additional a priori information and direct phase measurements by interferometry. Objective for all methods is to find the phase response as a function of the applied voltage and the local position at the SLM, i.e., ϕ(V,x,y).

A. Determination of the Phase Response from Intensity Measurement

As described above, for an ECB-mode LC-SLM there is ideally no twist of the LC molecules during operation. Therefore, the phase shift ϕ(V) at a given SLM position can be derived from a measurement of the amplitude modulation when the SLM is placed between crossed polarizers. The director of the ECB-mode LC-SLM has to be oriented at 45° relative to the crossed polarizer; see Fig. 2(a). Local transmittance measurement is done by an unexpanded laser beam passing through the ECB-SLM sandwiched between crossed polarizers, where the voltage-dependent transmitted optical power is detected by the detector.

Fig. 2. Determination of the ECB-mode LC-SLM phase response by intensity modulation measurement. (a) Optical scheme for transmittance measurement with a photodiode (PD) or an optical power meter (OPM). (b) Measured normalized transmittance Tnorm, determined discontinuous phase shift ϕdiscont., and continuous phase shift ϕcont. with ambiguities eliminated over applied voltage (from top to bottom).

With an input polarization matched to the orientation of the first polarizer, the ideal transmission of the parallel-aligned cell between crossed polarizers can be written as
T(V)=sin2[Γ(V)2],
(5)
where Γ(V) is the voltage-dependent retardation of the birefringent retarder given by Γ(V)=ϕ(V)=kdΔn(V) with the wavenumber k. By measuring the transmittance over a given voltage range, the phase shift ϕ(V) is then simply
ϕ(V)=2arcsin[T(V)12].
(6)

Note that there are ambiguities because of the inverse sine function in the phase-over-voltage characteristics, which have to be numerically eliminated by a continuous sweep. With a normalized transmittance 0Tnorm1, the ambiguities are identified by searching for local extremes in ϕdiscont. with a value close to 0 or π; compare with Fig. 2(b).

B. Interferometric Measurement of the Phase Response

Alternatively, interferometric methods can be utilized for phase-response measurement. In case of a transmissive LC-SLM, a Mach–Zehnder interferometer is best suited because it enables a single-pass measurement and a variable imaging field size.

Figure 3(a) shows the schematic experimental setup. Linearly polarized light coming from a laser (λ=532nm) is spatially filtered and collimated by a first lens. The interferometer input wavefront is then divided in amplitude by a polarizing beam splitter (PBS), where the p-polarized component is transmitted to the reference arm (upper right arm in the figure) and the s-polarized component is reflected into the test arm of the interferometer, where it transmits the phase-only LC-SLM under test. Both waves are recombined at the second PBS and interfere after passing through a 45° linear polarizer. It is important that the LC-SLM is imaged onto the CCD, hence the imaging optics in the interferometer exit. The magnification of the two-lens Kepler-type imaging optics determines the how large the area is, which is locally averaged. For a spatially resolved measurement, a high magnification that images only several tens of pixels should be chosen. The resulting interference pattern represents the phase difference between the reference and test wave. For phase calibration, the relative phase difference between the initial LC state and an actuated LC state is of interest. Therefore, the aperture of the LC-SLM, which is transmitted by the test wave, is divided into two parts: one subaperture remains unchanged (zero voltage, initial LC state, “reference area,” upper part in the right subfigure), whereas in the other part different phase values are adjusted (actuated state, “measurement area”). This is usually done by displaying a gray-level bitmap onto the LC-SLM, as schematically shown in Fig. 3(b). The resulting interferogram is depicted in the right column for a set of different actuation voltages. A phase shift within the actuated aperture will result in a shift of the interference fringes. This effect is best visualized if a carrier frequency is adjusted in the initial (00) state. A carrier can be easily introduced by slightly tilting of one of the mirrors. Measurements are performed for a set of different bitmaps, which introduce different phase shifts ϕ(V). By approaching the (02π) state, the pattern should be equal to that of the (00) state. The fringe shift ϕ(V) between the apertures is determined by interferogram cross correlation between the reference IR and measurement area IM.

Fig. 3. Mach–Zehnder interferometer for measuring the phase response.

Given that the two interferogram images (IR and IM are subsets of the entire interferogram) have the same dimensions of (m×n) pixels, the two-dimensional (2D) discrete cross correlation between IR and IM is formally given by
IXC(k,l)=i=1mj=1nIR(i,j)·conj[IM(i+k,j+l)],
(7)
where 1k2m1 and 1l2n1 [16

16. MathWorks, “2D cross-correlation,” http://www.mathworks.de/de/help/signal/ref/xcorr2.html.

]. The position (kP,lP) of the maximum absolute value of the cross correlation IXC reveals the relative lateral shift of the interference fringes in pixel units. With the indices (kP,lP), the relative shifts in row and column direction are given by Δk=kPm and Δl=lPn, respectively. To find the relative phase shift between IR and IM, its carrier frequencies fc|R, fc|M have to be known. By definition, fc|R=fc|M=fc because of the tilt, which has been adjusted in the initial off state for both areas equally. The carrier frequency fc=fcx2+fcy2 in line pairs per pixel of the interferogram images are determined by locating the peaks in the 2D discrete Fourier transform (DFT) of IR and IM, respectively. The voltage-dependent relative phase shift between both interferogram areas is finally then
ϕ(V)=2πfcΔk2(V)+Δl2(V).
(8)

When adjusting the carrier frequency of the interferogram, it is important to note that the accuracy of the evaluation method is influenced by quantization errors caused by the discrete operations of both the Fourier transform and the cross correlation. On the one hand, the more fringes in the interferogram, the more accurately the carrier frequency can be determined by the DFT at a given pixel number of the CCD. On the other hand, the cross correlation is more precise for larger periods of the interference fringes because it determines the relative shift in fractions of a single fringe period. Figure 4 shows some details of data analysis of the interferometric phase-response measurement. With a tilt of approximately eight to nine fringes over the aperture of 1280 pixels, good results in the numeric analysis were obtained.

Fig. 4. Details of the interferogram analysis for phase-response determination. (a) Captured interferogram for a certain voltage level with marked reference and measurement areas IR and IM. (b) Cross correlation of IR and IM. (c) Determined phase response for a series of interferogram pairs IR and IM at different voltage levels.

C. Functional Approximation of Inverse Phase Response

Regardless of which method is used to determine the phase response, the result is a continuous function of the phase shift ϕ in dependence of the applied voltage V, as illustrated in Fig. 2(b) or Fig. 4(c). However, to address the LC-SLM with a given linearly spaced phase distribution, the voltages that generate those shifts are of interest. To meet this need, the inverse function V(ϕ) is saved in the display driver electronics, usually as a look-up table (LUT). In Fig. 5, a graph of the inverse phase response is plotted.

Fig. 5. Graph of the inverse phase response, that is, the voltage-phase calibration curve V(ϕ).

From the measurement data, a modulation range over 2π is selected as indicated by the dashed lines in Fig. 5. Basically, any voltage limits Vmin, Vmax can be selected for which a modulation over 2π is achieved. For the sake of sensitivity it is of advantage to omit the areas close to the threshold voltage and close to saturation voltage. Here, the range 2π+ϕ0<ϕϕ0 with ϕ0=0.5rad have been selected. Within this range the curve has been approximated by an mth-order polynomial of the form
V(ϕ)=n=0man(ϕϕ0)n,
(9)
which is afterward recalculated at N linearly spaced phase values (0ϕ<2π) with N being the bit depth of the SLM’s addressing voltage. If no local variation of the phase response is present, this phase-voltage characteristic is usually stored in a LUT of the SLM driver electronics.

4. 2D Interpolation of the Set of V(ϕ,x,y) Curves

So far I have discussed two methods to determine the phase-voltage characteristics V(ϕ) independently from the local measurement position on the LC-SLM. If, however, there is a global variation in the phase response, such measurements have to be repeatedly taken at a sufficiently large number of different SLM positions. From preliminary observations of the LC-SLM it was known that only low-frequency, continuous variations occur over the SLM aperture. Although not every pixel needs to be calibrated, the sampling of the measurement positions is still a trade-off between the resulting accuracy and measurement effort. Moreover, the overall accuracy of the phase calibration depends on how well the phase-voltage characteristic V(ϕ) is represented between the discrete sampling points Pq(x,y) where the measurement has been performed.

The aperture of the SLM under study was divided into 4×3 square areas. At each area’s center, a phase-response measurement according to one of the methods described above has been applied, and its inverse phase response has been approximated by the one-dimensional polynomial given in Eq. (9) within the range 2π<ϕ0. To achieve a clear mapping, the normalized positions Pq(xn,yn) of the LC-SLM to the measurement beam were aligned by help of fiducial marks written as a bitmap onto the SLM. Figure 6(a) plots the 12 voltage curves versus the phase shift. As it can be seen, the required voltage for a certain phase value differs across the SLM aperture, with strongest variations of about 1 V for higher voltages close to a 2π phase modulation. This manifests again the need for a local phase calibration.

Fig. 6. V(ϕ,x,y) curves and their 2D interpolation plotted as phase responsiveness maps. (a) Set of V(ϕ) curves acquired at 12 SLM positions. (b) Selected 4 of 256 voltage maps V(ϕ,x,y) interpolated by Legendre polynomials.

In Fig. 6(b) the result of the 2D interpolation is exemplarily shown for 4 of 256 voltage maps V(ϕ,x,y). Each surface corresponds to a constant phase shift over the full SLM aperture (256 discrete levels between 2π<ϕ0) and its deviation from a plane parallel to the (x,y) plane is a measure for the local variation of the phase response. Note that x, y coordinates are normalized and that none of the 4×3 measurement locations are at the edge of the SLM. Areas outside of the outermost measurement points are therefore extrapolated by the Legendre fit, which is the reason for the corner of the upper level to be higher than the 4 V in Fig. 6(a). Because the lateral sampling of the local phase-response measurement with N=12 sampling points is relatively low, I found that a first-order Legendre polynomial fit with four polynomials (offset, x tilt, y tilt, astigmatism) is adequate. Outcomes of this 2D data interpolation step are hence a look-up matrix (LUM) comprising the Legendre coefficients for each of the 256 phase levels and the voltage range VminVVmax, which is required to address all phase values in the interval (2π,0] over the full LC-SLM aperture.

I will now explain how to address the issue of spatially different output voltages of the column driver that gives the desired phase level across the whole LCD panel.

5. Compensation of the Spatially Nonuniform Phase Response by Remapping of Phase Bitmaps

As the used LC-SLM uses active matrix driving, the electro-optical response curve (input gray level to output voltages) is normally provided by a gamma supply buffer of the panel electronics for negative and positive voltages separately [17

17. K. Blankenbach, “Active matrix driving,” in Handbook of Visual Display Technology, J. Chen, W. Cranton, and M. Fihn, eds. (Springer, 2012), pp. 441–458.

]. Because the same curve is applied to all pixels, the local variance in the drive voltages cannot be incorporated in the panel electronics directly. Hence the content to be displayed has to be artificially distorted in its gray level either using a graphics unit or directly in the content-generation unit.

For development reasons, the gray-level remapping step used here was not yet implemented in the graphics processing chain but in a separate software that converts an input gray-level bitmap B to its desired remapped output B. The LUM of Legendre coefficients and the required voltage interval [Vmin,Vmax], determined by step 2 of the calibration procedure, serve as input variables for the remapping process, which works as follows: First, all pixels are identified, which should represent the same gray value. Then the required voltages V(ϕ,xn,yn) are calculated by evaluation of the Legendre polynomials at those pixel positions, where normalized coordinates (|xn|1, |yn|1) sampled with the native display resolution are used. By running a loop over each gray level (e.g., 0–255 for an 8 bit bitmap), the voltages for each pixel position are calculated in sequence. Finally, the voltages are assigned back to gray levels by using the relationship
B=uint8{255VmaxVmin[V(ϕ,x,y)Vmin]},
(10)
where uint8 refers to the conversion operation of the expression within the brackets to an 8 bit unsigned integer data type. Bitmap remapping is illustrated in Fig. 7 at the example of a checkerboard pattern. Comparing the histograms of B and B it is obvious that the remapping is accompanied by a loss of bit depth. Because of the spread to represent black (ϕ=0) and white (ϕ=2π) levels, the remaining effective bit depth is approximately 7 bits for the calibration data of the current SLM panel.

Fig. 7. Gray-level remapping at the example of a checkerboard pattern with original gray levels of 0 and 255. Shown are the patterns and their corresponding histograms.

6. Experimental Results

Fig. 8. Photographed intensity modulation when gray-scale wedges are addressed onto the SLM. The SLM is white backlight illuminated and viewed through crossed ±45° linear polarizers.
Fig. 9. 2D image reconstruction of Fourier transform holograms (a) without and (b) with consideration of the local phase calibration.
Fig. 10. Holographic reconstruction from iterative phase-only encoded holograms displayed at the LC-SLM (a) without and (b) with local phase calibration. In the upper images the camera focus was set to +100mm (in front of display); in the lower images the focus was at 250mm (behind display).

7. Conclusion

Methods for measuring and compensating the nonlinear, position-dependent phase response of a transmissive, active-matrix-driven LC-SLM with phase-only modulation have been presented and experimentally verified. A position-dependent phase response might be caused by the driving scheme in combination with the given display architecture. The exact knowledge of the transfer function of applied voltage to the resulting phase shift is a matter of concern for SLMs used in digital holography. The measurement methods discussed in this paper distinguish between localized methods that either measure intensity or phase variations. Whereas phase measurements deliver the phase response more directly, intensity measurements are indirect methods from which the phase response can be derived. Those methods have been selected especially in view of their potential for up-scaling to larger display sizes.

Notwithstanding the method used to characterize the local phase response, efficient means for data interpolation and phase compensation are needed, especially for real-time applications such as holographic imaging and digital holography. I have presented polynomial fitting and representation in the interval (2π,0] of both the inverse phase response V(ϕ) and its spatial dependency V(ϕ,x,y) with only a small amount of calibration data required, which allows for future integration in the graphics pipeline of a display system. In experimental studies I could demonstrate the resultant improvements in holographic reconstructions when the calibration method has been implemented.

The presented techniques are equally applicable to other wavelengths and other polarity inversion schemes given that the local measurement area is small enough to cover only pixels with the same voltage polarity during measurement. Hence, a field-sequential full-color operation at native frame rate with a well-calibrated phase response will be enabled.

The author wishes to gratefully acknowledge the overall support of Hiromi Kato, Naru Usukura, and Yuuichi Kanbayashi from Sharp Corporation for providing dedicated SLM hardware and continuous technical help. I furthermore thank Robert Missbach from SeeReal for his valuable help in electronic driving, technical assistance, and fruitful discussions.

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S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.

20.

S. Reichelt and N. Leister, “Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging,” J. Phys. 415, 012038 (2013). [CrossRef]

OCIS Codes
(090.2870) Holography : Holographic display
(120.5060) Instrumentation, measurement, and metrology : Phase modulation
(220.1000) Optical design and fabrication : Aberration compensation
(230.3720) Optical devices : Liquid-crystal devices
(230.6120) Optical devices : Spatial light modulators
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: January 23, 2013
Revised Manuscript: March 11, 2013
Manuscript Accepted: March 12, 2013
Published: April 15, 2013

Citation
Stephan Reichelt, "Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators," Appl. Opt. 52, 2610-2618 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-12-2610


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References

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  19. S. Reichelt, R. Häussler, N. Leister, G. Fütterer, and A. Schwerdtner, “Large holographic 3D displays for tomorrow’s TV and monitors—solutions, challenges, and prospects,” in Proceedings of 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society LEOS 2008 (IEEE, 2008), pp. 194–195.
  20. S. Reichelt and N. Leister, “Computational hologram synthesis and representation on spatial light modulators for real-time 3D holographic imaging,” J. Phys. 415, 012038 (2013). [CrossRef]

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