High efficiency optical reconstruction of binary phase-onlyfilters using the Hughes liquid crystal light valve
Jeffrey A.-Davis, Gail M. Heissenberger, Roger A. Lilly, Don M. Cottrell, and Michael F. Brownell
The Hughes liquid crystal light valve (LCLV) has been evaluated for its applicability in writing and readingbinary phase-only filters (BPOFs) in optical correlators. Experimental measurements of relevant perfor-mance characteristics of the LCLV as well as experimental results demonstrating its use for reconstructingBPOF's are reported. We also find that this device allows a significant optical system throughput. Inaddition, we discuss generation of the BPOF with a MacIntosh computer system.
1. Introduction
Phase-only filters (POFs) have been shown toachieve superior performance in optical correlator sys-tems compared with fibers containing both amplitudeand phase information.4 '5 These theoretical studiesshow that, when the POF is used, the correlation signalis larger and gives superior discrimination betweensimilar objects, increased robustness in the presence ofnoise, and decreased sidelobes. Equally important isthe fact that these filters can, in principle, transmit100% of the incident light intensity in contrast withfilters having both amplitude and phase information.However, the same theoretical studies show that thesefilters also exhibit higher susceptibility to both scaleand rotation changes as well as lower SNRs.
An even simpler filter restricts the phase values tobinary values3 4 giving a binary phase-only filter(BPOF). Computer simulations using this filter alsoshow excellent correlations with a somewhat highernoise level. However, from an experimental view-point, the BPOFs are very easily implemented in realtime, using such commercially available programma-ble spatial light modulators (SLMs) as the magnetoop-tic SLM5,6 which is commercially available throughSemetex Corp. and the compact Japanese liquid crys-tal TV. 7 8
In both of these devices, the polarization axis forlinearly polarized transmitted light is rotated as it
When this work was done all authors were with San Diego StateUniversity, Physics Department, San Diego, California 92182; G. M.Heissenberger is now with Hughes Aircraft Company, EDSG, ElSegundo, California 90245.
passes through any electrically activated SLM element(defined as the ON state) relative to an unactivatedelement (defined as the OFF state) as shown in Fig. 1.In the usual operation of these devices, the analyzerpolarizer is oriented perpendicular to the OFF polariza-tion state, effectively blocking transmission for lightpassing through that element. Transmission will oc-cur for the ON polarization state. Therefore, individ-ual areas of the SLM can be made ON or OFF, and thetransmitted pattern will consist of both dark and lightregions.
Bipolar phase modulation can be obtained6 by ori-enting the analyzer polarizer perpendicular to the bi-sector of the two polarization states as shown in Fig. 2.The electric field vector for the transmitted light nowhas a 7r phase shift between the ON and OFF states. Inthis case, the transmitted beam will visually not ap-pear to have any pattern imposed on it since intensity,rather than electric field, is viewed.
11, Spatial Light Modulator Throughput
Although the above-mentioned devices have beenused to display bipolar modulation, an important con-sideration, which has not been adequately discussedpreviously, is the optical throughput of the SLM.Here throughput is defined as the percentage of inci-dent light which is transmitted through the device.This feature impacts the final system SNR and theamount of input optical power which is required for theoptical correlator system. This throughput dependson the rotation angle imposed by the SLM between theON and OFF states. When this angle is small, the per-centage of the light transmitted by the analyzer will bevery small.
If the angle between the ON and OFF polarizationstates is given by 2, the fraction of light intensity whichis passed by an ideal analyzer polarizer in the case ofbipolar modulation is given, using the Malus law, by
Fig. 3. Rotation angle of polarization plane for light reflected bythe LCLV vs the write light intensity. The LCLV operated at 10
Vrms and 10 kHz.
Fig.1. Orientation of analyzer polarizer to achieve ON/OFF modula-tion.
OFF ON
Lz.
(2(2(2
0i-
0
ANALYZER
POLARIZER
Fig. 2. Orientation of analyzer polarizer to achieve bipolar modula-tion.
T = sin2 (Q/2). (1)
For Q = 110, as in the case of the liquid crystal TV8 , thethroughput T is -0.9%. This value neglects through-put losses due to device absorption and the wire gridimposed on the device. Therefore, some previouslydiscussed advantages of these phase filters includinghigh speed programmability and discrimination abili-ty must be weighed against the throughput loss. Wealso note that the throughput increases as the angle Qincreases and reaches 100% when Q = 1800.
The Hughes liquid crystal light valve (LCLV)9 isalso capable of encoding both phase and amplitudeinformation.'l In an effort to examine the LCLV forbipolar modulation, we measured the polarizationstate of the reflected light as a function of write light'intensity.
111. Characteristics of the Hughes LCLV
The Hughes LCLV has been thoroughly discussedelsewhere9 and will not be covered here. It differsfrom the other SLMs discussed earlier in that it isoptically addressed by a writing light beam rather thanbeing electrically addressed. The write light intensitywas obtained using either a Cyonics air cooled argon
120-
100 -
800
60
40 t
20
0
0 10 20 30 40 50 60 70 80 90 100
WRITE INTENSITY ( iW /cm2
)
Fig. 4. Rotation angle of polarization plane for light reflected bythe LCLV vs the write light intensity. The LCLV operated at 7
Vrms and 1 kHz.
laser filtered to obtain the 514.5-nm output or a whitelight beam optically filtered with a 514.5-nm interfer-ence filter. A He-Ne laser was used for the read beam.The incident He-Ne beam was slightly tilted relativeto the face of the LCLV to achieve spatial separation ofthe reflected and incident beams. The reflected beampassed through a linear polarizer which analyzed itspolarization state. In this experiment, the LCLV wasbiased as recommended by the manufacturer with 10Vrms at a frequency of 10 kHz.
As shown in the Fig. 3, the principal polarization axisof the reflected light rotated approximately linearlywith increasing write intensity, reaching a maximum of.70° at a write intensity of 100 ptW/cm2. This value ofQ indicates that the transmission through the analyzerpolarizer is now 33% and represents an improvement inthe throughput by a factor of -35 compared with theLCTV.
The polarization state of the reflected beam fromthe LCLV became slightly elliptical as the write inten-sity increased. With no write intensity, the ellipticity(defined as the ratio of the intensities parallel andperpendicular to the major axis of polarization) was-50/1. As the write intensity increased to 100 ,uW/cm2, this ratio fell to -10/1. Next, both the bias volt-age and frequency were altered" to 7 Vrms and 1 kHzto produce a different operating condition as shown inFig. 4. As before, the rotation of the principal polar-ization axis is plotted as a function of write intensity.Several differences are seen. The maximum rotation
Fig. 6. Fraunhofer diffraction pattern for ON/OFF grid in Fig. 5.
angle was no longer linear with intensity but saturatedat low write intensities. The maximum rotation angleincreased to .102° giving a throughput of 60%. Theellipticity exceeded 50/1 over the entire range of inputwrite intensities. Obviously, the throughput in-creased dramatically with no increase in beam elliptic-ity. Previous measurements" indicate that the riseand fall times are not appreciably affected when theoperating voltage and frequency for the LCLV arechanged. We are presently investigating these alter-native operating conditions in much greater detail.
IV. Fraunhofer Diffraction Studies
We next examined the effect of ON/OFF modulationand bipolar modulation on the spatial frequency dis-tribution of the light reflected from the LCLV. Thiswas accomplished by imaging a Ronchi ruling onto thewrite side of the LCLV. The light reflected from theread side of the LCLV was examined in the Fraunhoferdiffraction plane in a manner similar to that reportedpreviously with the liquid crystal TV8 to determine itsspatial frequency distribution.
As a result of the binary spatial distribution of thewrite light due to the Ronchi ruling, the read lightreflected by the LCLV has two polarization statesseparated by an angle dependent on the write lightintensity. ON/OFF modulation is obtained by passingthe reflected read light through a polarizer oriented asshown in Fig. 1. This orientation completely blocksthe light reflected from regions of the LCLV which arenot illuminated by the write light. The resulting elec-tric field pattern reflected by the LCLV is shown inFig. 5. The Fraunhofer diffraction pattern for thisconsists of a high dc peak with first-order peaks whoseintensities are theoretically 4r 2 smaller than the dcpeak. Experimental results shown in Fig. 6 verify this.
0
I
'9
LI
L.
P:cW
7HHLLL. . . . 7 Position
Fig. 7. Transmission vs position for bipolar modulation grid pat-tern.
Position (full scale is 3.2 mm)Fig. 8. Fraunhofer diffraction pattern for bipolar grid pattern in
Fig. 7.
Bipolar operation of the LCLV is achieved by orient-ing the analyzer polarizer perpendicular to the bisectorof the two reflected polarization states as shown in Fig.2. In this case, the reflected electric field for theRonchi ruling is shown in Fig. 7. The Fraunhoferdiffraction pattern for this should have no d compo-nent. Results are shown in Fig. 8 and show a dramaticreduction in the size of the d peak relative to Fig. 6.
Although the size of the d term is greatly reduced,there is still some d transmission. One possible ex-planation for this is a slight spatial nonuniformity inthe write beam intensity. Since the rotation angle ofthe reflected light is dependent on the write beamintensity, a nonuniform writing intensity distribution(or a gray scale input pattern) results in a distributionof the rotation angles for the ON polarization states..Note that the OFF state always has the same polariza-tion direction. Therefore, bipolar modulation canonly be achieved exactly for one ON state intensity.These results were obtained using the operating condi-tions recommended by the manufacturer as shown inFig. 3. The consequence of operating as shown in Fig.4 would result in a constant rotation angle for a grayscale input pattern and a lower d diffraction peak.
Another explanation for the small d peak is thepolarization ellipticity induced in the reflected beam.As a result, the small orthogonal polarization statewould not be blocked by the second polarizer.
V. Use of the LCLV with Computer Generated BinaryPhase-Only Filters
Next, this device was tested with a BPOF which waswritten on the write side of the LCLV. The BPOF wasgenerated using a MacIntosh computer. An inputpattern having 128 X 128 pixels was directly composedon the MacIntosh screen. Figure 9 shows a typical
input pattern consisting of the letter R. The 2-DFourier transform was calculated in 100 s using 32-bit fixed point arithmetic.
The FFT algorithm gives the lowest components ofthe x and y spatial frequencies in the corners. Howev-er, the desired filter must have the zero spatial fre-quency at the center of the system to coincide with thezero spatial frequency position of the optical system.Therefore, the algorithm was altered to move the ori-gin to the center of the pattern.
The BPOF was generated by assigning a value of +1to a pixel if the real part is positive and -1 if the realpart is negative. This is equivalent to assigning +1when the phase is in the first or fourth quadrants and-1 when it is in the second or third quadrants. Theresulting BPOF for the original input of Fig. 9 is shownin Fig. 10. There are substantial savings in the storagerequirements using the binary phase-only filter.4 Inour case, the originally calculated FT required 128Kbytes of disk storage. By contrast, the BPOF onlyrequired 2K bytes.
The forward Fourier transform of this pattern wastaken by the computer to allow comparison with theoptically generated pattern and is shown in Fig. 11.
F -:
Fig.11. Computer generated impulse response of the BPOF for thetest object.
The original pattern and a ghost image are both gener-ated due to the real nature of the binary FFT.3 Oursoftware allows a variable threshold to be implement-ed in which all values less than this threshold are notprinted. This is optically equivalent to varying theexposure time of photographic film and was used toobtain Fig. 11.
The computer generated forward Fourier transformof the BPOF shows substantial edge enhancement asdiscussed earlier.3 This feature arises from the binarynature of the filter and can be easily understood. As-sume for convenience that the original input pattern isa square wave function. The Fourier transform of thisis the familiar sinc pattern [sin(x)x]. In this case, thehigher frequencies in the Fourier transform which de-scribe the sharp edges of the square wave are dampedby the l/x term in the sinc function. However, whenwe binarize the phase, we only consider the sign of thesinc function regardless of the magnitude. Therefore,the BPOF acts as a high pass filter resulting in edgeenhancement.
Next, a photographic transparency containing thisBPOF was placed in the write beam for the Hughesliquid crystal light valve. Again, the analyzer polariz-er was rotated to achieve bipolar operation for thereflected light. The reflected beam was sent through a35-cm lens, and the reconstructed Fourier transform ofthe BPOF could be viewed in the focal plane of thelens. The reconstructed image was magnified andrecorded photographically as shown in Fig. 12. Itcompares well with the computer generated pattern inFig. 11, including the high pass filtering discussed ear-lier.
VI. Conclusions
In conclusion, our experiments show that the liquidcrystal light valve is very well suited for use with binaryphase-only filters in optical correlator systems. Ourresults show excellent reconstruction of the BPOFwith excellent optical efficiency or throughput. Wealso note that the liquid crystal light valve has a veryhigh resolution. Using a typical value of 20 lines/mmat 50% normalized MTF 9 and a 25-mm size, the LCLVis capable of 500 X 500 pixels.
Fig. 12. Optically generated impulse response of the BPOF for thetest object.
In addition, we have demonstrated techniques forgenerating the BPOF using a MacIntosh computersystem.
We wish to thank W. Bleha and Hughes Aircraft foruse of the liquid crystal light valve, Mary Hatay for
assistance in preparing the slide transparencies of theCGH, and Mark Hatay for technical assistance. Wealso thank the reviewers of this manuscript for helpfulsuggestions, particularly regarding the dc peak in Fig.8.
References
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