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Computer-generated binary phase-only filters with enhanced light efficiency recorded in silver halide sensitized gelatin

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Pure Appl. Opt. 2 (1993) 595-605. Printed in the UK

Computer-generated binary phase-only filters with enhanced light efficiency recorded in silver halide sensitized gelatin J Campost, B Janowska-Dmocht, K Styczynskis, I( Chalasinska-Macukowt, F Turonll and M J Yzuelll

t Department of Physics, University of Barcelona, Diagonal 641, 08028 Barcelona, Spain

t Department of Chemistry. Warsaw University, AI.Zwirki i Wigury 104,02-089 Warsaw, Poland 5 Institute of Geophysics, Department of Physics, Warsaw University, Pasteura 7, 02-093 Warsaw, Poland 1) Department of Physics, Autonomous University of Barcelona, 08193 Bellaterra, Spain Received 4 March 1993, in final form 11 May 1993 Abstract. The silver halide sensitized gelatin (SHSG)technique of bleaching is proposed for producing computer-generated binary phase-only filters with enhanced light efficiency. A comparison of light efficiency and recognition results lor amplitude- and phase-recorded filters is presented.

1. Introduction

During the last 20 years correlation methods have played a very important role in optical information processing. Using digital methods one can easily encode and modify filters, depending on the application [l, 21. The computer-generated holography technique [3] involves generation of transparencies with a desired amplitude transmittance. Since the transmittance is a complex function, it must be coded because most devices modulate only the intensity. The binary encoding of the phase-only filter, or its binary version, is one of the best candidates for application in optical pattern recognition [4-61. However, amplitude recording of filters limits the light efficiency of optical correlators. The use of phase materials for spatial-filter recording allows better utilization of laser light in the recognition system and keeps laser power requirements low. One suitable non-expensive phase material for this purpose is dichromated gelatin [7,SI. In comparison with the conventional bleaching techniques, dichromated gelatin assures higher diffraction efficiency, lower noise and no tendency to darken on exposure to light. However, dichromated gelatin has relatively low sensitivity and limited spectral response. The silver halide sensitized gelatin (SHSG)technique proposed by Hariharan [SI allows one to obtain efficient phase recording. Since the filter is recorded in a silver halide emulsion layer, the wide range of spectral sensitization available with commercial photographic materials may be used. The energy requirement is low and similar to that for conventional bleached holograms. The end product has the properties and structure of a dichromated gelatin hologram. It has been shown recently [lo, 111 that the quality of the matched filters recorded optically and fabricated by the SHSG technique is satisfactory. 0963-9659/93/060595t 11 $7.50

0 1993 IOP Publishing Ltd

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It is well known [12] that in general the phase recording of a hologram introduces some distortions which cause deformation of the reconstructed object. This means that phase-recorded matched filters have the impulse response deformed, and because of this have limited application in correlation methods [13]. Good recognition results are obtained only if the parameters of the phase-recorded filter are properly chosen and controlled [ll]. However, in the case of binary encoding the impulse response of the binary phase-recorded filter is no more disturbed than the impulse response of the amplitude version [12]. For this reason binary masks generated by computer and fabricated in phase materials allowing high light efficiency are ideal for many applications, including optical information processing [14, 151 and optical computing [16, 171. In this paper the SHSC technique is proposed for producing computer-generated binary phase-only filters (BPOF)with enhanced light efficiency. The filters are encoded by Burchardt’s method [lS]. The inverted image of the reference target, typical for the impulse response of the BPOF, is eliminated by encoding a Fresnel phase plate lens onto the BPOF [19]. Comparison of light efficiency and recognition results for both amplitude and phase recording of the BPOF are presented.

2. Binary phase-only filters

Let the reference target g(x, y) have the Fourier transform C(v, p) = IC(v, p)l exp[i4(v, p)] where IG(v, p)l and +(v, p) are the amplitude and the phase of the Fourier transform of the target, respectively. According to Horner’s definition [20] the phase-only filter HpOF(v,p ) has the form &F(v>

P ) = exp[-i4(v.

AI’

(1)

The binary version HBpoF(v,p ) of the phase-only filter [21] defined by the formula

yields a binarized version of a cosine filter [22]. This means that the impulse response consists of the target and its inverted version. Therefore the output signal in the correlation plane is the result of correlation of the input object with the target and an inverted version of the target. One of the methods for eliminating correlation of the input object with the inverted image of the target is the encoding of a Fresnel phase plane lens onto the BPOF [19]. A Fresnel phase plate lens having a focal length z is generated by using the function

The Fresnel lens encoded binary phase-only filter (BPOF-L)for a target g(x,y) is generated by forming the following filter function HPOF.L(V, P) = Z*(V,P)HPOF(V, P).

(4)

The corresponding binary version HBPOF.L is also a cosine filter, but the introduction of the Fresnel phase plate lens causes defocusing of the correlation signal of the input object with the inverted version of the target in the output plane.

SHSG

computer-generated binary phase-only filters

3. Amplitude-recorded and phaserecorded

BPOF coded

597

by Burckhardt’s method

The two kinds of binary filters mentioned above, BPOF and BPOF-L, are encoded digitally using Burckhardt’s method. Burckhardt’s coding scheme to produce computer-generated holograms belongs to the family of detour phase encoding methods [3], and is based on the decomposition of a complex value into three complex numbers with positive amplitude and phases equal to 0, $ and $c [IS]. This means that the complex transmittance A exp(i4) of each pixel of the filter is replaced by the superposition of three complex numbers: A exp(i4)

= A,

+ A , exp(i$x) + A , exp(i$z)

(5)

where A,, A , and A , are real and positive numbers. The binary phase-only filter [20] has uniform amplitude and the phase takes only two values, 0 or n. Thus, the complex transmittance A exp(i4) can be obtained by superposition of only two complex numbers: exp(i4) = k, + A; exp(ix).

(6)

The coefficients Ai take only two values, 0 or 1, which means that each pixel of the filter is represented by a cell which has two apertures (figure 1) with transmittance 0 or 1 . Thus we obtain a binary mask. The transmittance d,(n s) of the cell corresponding to the j , k pixel of the filter is described by [3]

where p. v and Sp, 6v are the coordinates in the filter plane and the cell dimensions, respectively. In the case of amplitude recording the coefficients ajr are real and positive and take values aj.,(0) = 1, aj,x(l) = 0 for the phase value 4 = 0, and aj,k(0)= 0, aj,J1) = 1 for the phase value 4 = x (see figure 1). In the case of phase recording the coefficients aj,r are complex and take the form aj.dp) = ex~Ci@~,&~)l.

(8)

The transmission of both apertures of the encoded cell is 100% and only the phase shift A@ between them equal to A@j,k= @j,!(0)- @j,h(l)is introduced. This means that aj,x(0)= exp( - iix) and aj,,.(1) = exp( &) for 4 = 0, whereas aj,,(0) = exp( + i h ) and aj,k(l)= exp( -&), for 4 = x. The transmittance ?(& v ) of the filter which has the form of a binary mask, is [3]

+

IMP-1

?@,

(NP-1

v) = j=-M/2 h=-N/2

0

-

cj,,(p- j ap, v

- k SV).

n

Figure 1. Cell struclure with two components encoding two phase values 0 or a.

(9)

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The impulse response r ( x , y ) of the filter takes the form: (.WIZ)-1 ( N / Z ) - l

T ( x ,Y ) =

C

j = -MI2

C

t = -NI2

where $Jx,

+y(Wl}

Cj,dx,Y ) exp{2ni[x(.i6~)

(10)

+

y ) = $&I 6v sinc($x 8p) sinc(y 6v)(uj,,(0) a,,,+( 1) exp[2ni(x 6p)/2]} (11)

cjj.k(v,

is the Fourier transform of the transmittance of the cell p), We see that to obtain the impulse response of the binary filter using equatiohs (10) and (1 1) it is necessary to calculate only the Fourier transform of the rectangular coding aperture, because each coded ceU contains only two identical apertures with different uniform transmissions [23]. This remarkably reduces the time of calculation in comparison with the general case, in which usually it is necessary to calculate M x M Fourier transforms. 4. Light efficiency of the phase-recorded BpoF-digital simulation

If we discuss the light efficiency of a binary hologram it is necessary to consider that, in practice, the contrast of a device is limited, and the coded cell usually does not have transmission values 0 or 1, but takes two distinguishahlk real positive values aj,JO) and ~ ~ , ~ The ( l ) intensity . of reconstructed images is proportional to Iaj,,(O) - aj.,(l)lz and reaches a maximum for the case in which the transmissions are zero and one [3]. If the photographic processing includes bleaching and the coefficients aj,J0) and aj,,(l) are complex, the image intensity is maximized when the phase modulation depth is just TI and reaches an intensity four times higher than that obtainable in the amplitude case [3]. In the case of phase recording the intensity of reconstructed images depends nonlinearly on the depth of the phase modulation A$ [24J Figure 2 shows the PHASE- RECORDED

DEPTH

BPOF

OF PHASE MODULATION I x T I I

Figure 2. Diffraction eBciency of BPOC as a function of the depth of the phase modulation -digital simulation: 0 ,input energy; W, energy diffracted into - 1 and 1 order; V, zero order energy.

+

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computer-generated binary phase-only filters

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Figure 3. Input scenes: (a) the upright abject (‘butterfly 1’) and its inverted version: (b)two different objects (‘butterfly I ’ and ‘buttemy 2’).

diffraction efficiency of the phase-recorded BPOF obtained digitally by using formulae (10) and (11). The filter has been matched to the ‘butterfly 1’ (figure 3(a)). The dimensions of the input matrix are 128 x 128. The input energy corresponding to the total energy in figure 2 is normalized to unity. The intensity of zero and first diffraction orders has been calculated as a function of the depth of the phase modulation A ~ j , k The image intensity of the first diffraction order is calculated taking into account both diffraction waves. We see that in the case of phase recording the first order may reach a much higher intensity than the zero order. For the depth of phase modulation equal to x, about 30% of the total energy is going to each first order, whereas the intensity of the zero order is about 10%. In comparison, a regular rectangular phase grating with the phase modulation equal to x provides 40% of the total energy in each first-order diffraction and at the zero order the intensity is equal to zero [24]. The diffraction efficiency presented in figure 2 is used in experiments for the phase modulation depth estimation of fabricated filters.

5. Experimental results

5.1. Filter recording

In our experiment a laser printer HPLaserJet 111 has been used to plot the filter characteristics [5, 251. The resolution of the laser printer is 30M) DPI. The dimension of the filter is 128 x 128 pixels. The dimension of the final filter obtained by the laser printer

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is approximately 180 x 180 mm'. The filter is photographically reduced t o approximately

5

x 5

mm2 before using it in an optical correlator. In order to obtain phase recording of the binary phase-only filters we have used the method proposed by Hariharan [SI. Filters have been recorded on 649F holographic Kodak plates and bleached using the bleaching procedure presented in table 1 111, 151. One of the BPOF filters fabricated by the proposed method is shown in figure 4. The phase distribution of the BPOF filter is recorded by phase-contrast microscopy. We can see that the edges of the coded cells are well defined and are not destroyed by the bleaching procedure.

Table 1. Bleaching procedure. All solutions at 20 "C.

Time (min)

Step

I Develop, Kodak D-I9 2 Rinse, running water 3 Bleach, in batch: Potassium dichromate 1.6 g Sulphuric acid 2.0 ml Distilled water 1.0 I 4 Rinse, running water 5 Fix. Agfa-Gevaert G334 h Wash, running water 7 Rinse 50% isopropanol 50% distilled water 8 Dehydrate, loo"< isopropanol 9 Dry, in air 10 Bake. 70°C

Figure 4. Phase dimbutton or the

5

I

1 5 IO

3

3 5

20

"Pot

filler recorded by phase-contrast mlcroscapy

Table 2 shows the comparison of the amplitude- and phase-recorded and takes into account:

BPOF-L,

BPOF

and

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computer-generated binary phase-only filters

Table 2. Transmission, relative difraction efficiency, and PRSMR for amplitude and phase recording Theoretical value of transmission in parentheses.

Filter

PRSMR’

amplitude phase BPOF-L amplitude BPOF-L phase BPOF BPOF

1.0 11.8 1.4 12.7

12 (50) 84 (100) 9 (50) 83 (100)

1.0 0.5 3.1 0.8

(1) theoretical and measured values of the transmission of the filters defined as the ratio of the total transmitted energy I , to the total incident energy 1:; (2) relative diffraction efficiency q/q., where qs is the diffraction efficiency of the amplitude recorded BPOF; and (3) the level of noise in the correlation plane estimated by the peak-to-root mean square ratio (PRMSR) [26, 271 defined as PRMSR =

GO, YRMS

12)

where C,,, is the correlation peak energy, and yRMsis defined according to

i2 denotes the set of output pixels for which the output values are below 50% of the peak value and N, denotes the number of pixels in this set. Theoretical values of transmission presented in brackets in table 2 correspond to the ideal recording in which zero and one of the binary masks have 0 or 100% of the transmission in the case of amplitude recording, or 0 or II phase shift in the case of phase recording. In such ideal conditions the phase-recorded filter attains a diffraction efficiency four times higher than that obtainable with amplitude recording [3]. In our experiment the measured values of transmission in the case of amplitude recording are remarkably lower. This means that the coded cell takes on two distinguishable values of transmission, but this case does not correspond to the maximum of modulation. The absolute value of the diffraction efficiency is about 3% instead of 12% predicted theoretically. In the case of phase recording the measured transmission is also lower in comparison with the theoretical value. The transmission of the final product is less than 100%. The loss of light is not due to the small phase-modulation depth, but results from the limited optical transparency of the bleached filter and some parasitic reflections. To estimate the phase modulation of the phase-recorded BPOF and BPOF-L we have used the characteristics shown in figure 2. The values of the absolute diffraction efficiencies measured in zero and first orders for both filters, BPOF and BPOF-L, were the same: 30% for zero order and 40% for the sum of the two first-order diffraction waves, this corresponding to phase modulation greater than n/2. Thus, we compare two kinds of filters with limited amplitude or phase contrast and it is for that reason that the phase-recorded filters have a diffraction efficiency more than 10 times higher than amplitude-recorded filters (table 2). It is also necessary to

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mention that it is much easier to improve the light efficiency of the filter using phase recording than to try to optimize amplitude recording, which is always limited by the contrast of the devices. This means that, in the case of bleached filters, by using an SHSG method we are able to fabricate filters with enhanced light efficiency, even for a phase modulation depth lower than li.

5.2. Optical prrtrrrrz recognition The second step of the experiment has been concentrated on optical recognition. Two kinds of binary phasc-only filters, BPOF and BPOF-L, have been applied to this purpose, both obtained by the SHSG technique. The input scenes to recognize are shown in figure 3 ( a ) and 3(h). All filters are matched to the ‘butterfly I’. The input scene shown in figure 3(aj consists of the upright object (‘butterfly 1’) and its inverted vcrsion and is applied to show thc influence of the coded lcns for the correlation results. Digital analysis has shown the same influence of the lens for both cases, amplitude- and phase-recorded filters. The digital results for phaserecorded filters and the corresponding optical results are presented in figures S and 6. We obtain two peaks in the output plane of the correlator (figure S(a)). The upright object is correlated with the upright version of the ob.iect contained in the BPOF filter. while the inverted object is correlated with the inverted image o l the ‘butterfly I ’ contained in the BPOF. When the Fresnel lens encoded RPOF (RPOF-L) was used, one peak of the correlation in the output plane was strongly rcduccd (figure 5(h)j because correlation with the invertcd version of the object contained in the RPOIFI, was remarkably degraded by defocusing. The reduction of thc correlation peak corresponding to the inverted version dcpends, ofcourse, on the focal length of the Fresncl lens encoded onto thc RPOF-L. I n this case the power of the Fresnel phase platc lens with a focal length equal to 6 m was too small to eliminate fully the second correlation peak. Optical results (figure 6) obtained for amplitude- and phasc-recorded filters are also

Figure 5. Inlluence 01 the encoded lens on the corrclalion phasc~rccordedfilters: ( U ) ”POP; ( h ) BPOF-L.

TC\LI/I~

-digital simiilafion lor

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computer-generated binary phase-only filters

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Figure 6. Optical results for recognition obtained for the input scene shown in figure 3(a): amplitude-recorded filters (a) BPOF; (b) RPOT-L; phase-recorded filters (c) BPOF; (d) BPOF:L.

similar, and confirm the prediction of digital analysis that in both cases the properties of the filters are the same. We observe only some increase of the level of noise in the correlation plane which is higher in the case of the phase recorded filter (see table 2). To eliminate the non-desired phase variations, all filters have been introduced into the liquid gate during optical processing. The resulting correlation data have been recorded by a CCD camera and stored and processed in a PIP Matrox video digitizer board interfaced to a microcomputer and Laserprinter LaserJetIII. The second input scene shown in figure 3(h) consists of two different objects,

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Figure 7. Optical results far recognition obtained lor the input scene shown in figure 3(h): case; ( h ) BPOF-L case.

((I) BPOF

‘butterfly 1’ and ‘butterfly 2’. In both cases, BPOF and BPOF-L, the recognition is satisfactory (figure 7). A s was predicted theoretically, phase recording of the binary filters did not degrade the recognition capability of the optical correlator.

6. Conclusions In this paper the SHSG technique is proposed to obtain computer-generated binary phase-only filters with enhanced light efficiency. The end product has the properties and structure of a dichromated gelatin mask, but since the filter is recorded in a silver halide emulsion layer, the wide range of spectral sensitization available with commercial photographic materials may he used. Theoretically, the bleaching procedure will give a light efficiency only four times better than for amplitude recording, hut in practice the increase can he much higher. Usually the contrast of the amplitude recording devices is limited and maximum modulation is impossible to obtain. Phase recording, however, assures satisfactory light efficiency even if the depth of phase modulation is far from the maximum. In the case of the binary mask the bleaching procedure does not introduce any additional deformation of the impulse response of the filter and the recognition results are satisfactory.

SHSG computer-generated

binary phase-only filters

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Acknowledgments The authors thank Esmail Ahouzi for his fruitful help during the experiment. This work has received partial financial support from the Spanish CICYT (Commission Interministerial de Ciencia y Tecnologia) Project number ROB90-0887-C02-01and from the Polish Scientific Committee Project number 20 92 49 101. References [I] Vijaya Kumar B V K 1992 Appl. Opt. 31 4773-801 [?I Campos J. Turon F, Yaroslawsky L P and Yzucl M J 1993 Int. J . Opt. C o m p t . to be published [3] Dallas W 1980 Computer-generated holograms 7he Computer in Optical Research-Methods and Applications (Topics in Applied Physics 41) ed B R Frieden (Berlin: Springer) pp 291-366 141 Flavin M A and Horner J M 1989 Appl. Opt. 28 1692-6 [SI Campos 1,Turon F, Yzuel M J and Vallmitiana S 1990 Appl. Opt. 29 5232-4 161 Campos 1. Turon F and Yzuel M J 1992 App/. Opt. 31 3337-43 [7] Homer J L 1982 Appl. Opt. 21 4511-14 181 Yang G.Fu S and Su Y 1986 Prm. SPIE 673 554-6 [9] Hariharan P 1986 Appl. Opt. 25 2040-2 [IO] Chalasinska-Macukow K, Piliszek J and Janowska-Dmoch B 1989 Opt. C o m n 74 25-30 [Ill Janowska-Dmoch B, Chalasinska-Macukow K and Piliszck J 1992 J , Opt. h e r Tecknol. 24 279-84 [I21 Bryngdal 0 and Wyrowski F 1990 Digital Hologrupky-Computer Generuted Holograms (Progress in Optics XXVIII) cd E Wolf (Amsterdam: Elsevier) pp. 3-86 [I31 Valcra M S Land Kwasnik F 1988 J. Phys. D: Appl. Pkys. 21 S187-90 [14] Brandstctter R and Lcib K 1991 J. Opt. h e r Tecknol. 23 247-50 [IS] Campos J, Janowska-Dmoch B, Styczynski K, Turon F, Yzucl M J and Chalasinska-Macukow K 1991 Proc. SPIE 1574 141-7 1161 Streibl N 1989 J. Mod. Opt. 36 1559-73 [17] Ichikawa H, Taghizadch M R and Turuncn J 1991 Opt. E n g q 30 1869-77 [18] Burchardl C B 1970 Appl. Opt. 9 1949-50 1191 Davis J A, Cottrell D M, Lilly R A and Connely S W 1989 Opt. Lett. 14 659-61 [20] Homer J L and Gianino P D 1984 Appl. Opt. 23 812-16 [ll] Homer J L and Leger J R 1985 Appi. Opt. 24 609-11 [U] Cottrell D M, Lilly R 4 Davis J A and Day T 1987 Appl, Opt. 26 3755-61 [23] Styczynski K 1992 MSc thesis Warsaw University (in Polish) [24] Collier R J, Burckhardt Ch B and Lim L H 1971 Opticul Holoqrupky (New York: Academic) 223 1251 Lee A 1 and Casasent D P 1987 Appl. Opt 26 136-8 1261 Kumar B V K V and Hassehrook L 1990 App/. Opt. 29 2997-3006 [27] Homer J Land Bartell H 0 1985 Appl. Opt. 24 2889-93