For simplicity the effect of the aperture of the input object was omitted when Eq. Assuming a square aperture, then the right-hand side of Eq. Figure 3 a shows a 3-D This can be expanded in a Fourier series, plot of the diffraction spectrum observed when the phase shift is n-. The small dc peak shown may come either from the dc term in Eq. Figures 3 b and 3 c show results obtained under the same conditions as Figure 3 a , but with the open to closed ratio of the grating being and , respectively.
This is important from a practical point of view, since a thresholded JTPS more resembles a grating with an open to closed ratio which deviates from a Ronchi grating. Thus the output correlation peak, at most, will have the structure shown in Figure 3 b or Figure 3 c instead of the structure shown in Figure 3 a.
Once the phase shift parameters are known in terms of the brightness control voltage, polarization direction, and zyxwvuts When this. This pattern is then bin- arized and displayed back on the LCTV.
Figure 4 a shows the binarized JTPS and 4 b shows the correlation output due to the input images shown in Figure 1. I t should be noted that only the k1 diffraction orders are shown. The analysis zyxwvutsrq shows that, beside a delta spike at the origin, which can be where A is a constant, and JJ.
If the scene described by Eq. The Fourier transformed, it can be seen that aside from a pro- intensity of the output correlation peaks depends on the mod- portionality constant, an infinite number of diffraction orders ulation depth of the phase. The performance is better com- occur along the x axis, due to the convolution of the Fourier pared to the amplitude modulation case in terms of light uti- transform of the Fourier-Bessel series shown in the square lization since there is no need to use an analyzer that reduces brackets above.
The presence of infinite harmonic terms was the output intensity. It is clear from the results of Figures also predicted by Javidi [ll]using a nonlinear analysis.
Both used the same dc block mostly affects the dc peak in the correlation plane, which can always be eliminated by a dc block, it may also reduce the zyxwvuts correlation peak intensity.
Thus practically there is a need to zyxwvutsrq zyxw Figure 3 The diffraction orders of a phase Ronchi grating, b phase grating with open to closed ratio , and c open to closed ratio 7 : 3 introduce a simple algorithm to find an optimum threshold level, especially in a programmable JTC environment, in or- der to get higher diffraction efficiency correlation outputs. Army Missile Command through the U. Army Research Office, under Contract No. DAAL, is gratefully acknowledged.
Its open to closed ratio depends on the thresh- support of the Direccion General de Investigacion Cientifica olding condition set in Eq. Yu, S. Jutamulia, T. Lin, and X.
Laser Technol. John zyxwvut 2. Konforti, E. Marom, and S. Lu and B. Liu, J. Davis, and R. Gregory, J. Loudin, J. Kirsch, E. Tam, and One of these phenomena is the great difference of the F. Generally the 6. Lin, and D. In this paper, a new and rigorous 7. Javidi and J. Tam, F. Yu, and D. All possible move- Tanone, C. Uang, F. Yu, E. Tam, and D. Log in with Facebook Log in with Google. Remember me on this computer. Enter the email address you signed up with and we'll email you a reset link.
Need an account? Click here to sign up. Download Free PDF. Phase modulation in a liquid-crystal TV based joint transform correlator Microwave and Optical Technology Letters, Don Gregory. A short summary of this paper. Download Download PDF. Translate PDF. Microwave Theory Tech.
MTT, , pp. I n this phase modulation scheme there is no need to use a polarizer-analyzer like the one used in the binary phase modulation scheme [4]. In a recent article we have reported some experimental results using this phase modulation prop- 2.
Caorsi, G. Gragnani, and M. H, Vol. MTT, The joint transform architecture is well known in optical pro- cessing. Normally the two objects t o be correlated are as- zyxwv MTT- the input plane of a joint transform correlator. If the two 33, , pp. Sarkar, D. Weiner, and V. Antennas Propagat, Vol. AP, , pp. The correlation output is obtained by taking the Fourier transform of the above power spectrum.
However, in this case they are displayed on an LCTV that can modulate phase. Gregory and J. Yin, P. The joint transform power spectrum is modeled as a binary phase object to calculate the correlation output.
The results have been experimentally verified using a liquid-crystal television operating in the phase modulation mode. It is clear that except for the delta spike at the origin and the proportionality constant, the JTPS has the same form as that of the amplitude object given by Eq. The delta spike at zy 6 of a twisted nematic liquid-crystal cell and the cell is operated the origin will saturate the square-law detector to the point that the high-frequency, low-amplitude fringes may be lost.
For simplicity the effect of the aperture of the input object was omitted when Eq. Assuming a square aperture, then the right-hand side of Eq. Figure 3 a shows a 3-D This can be expanded in a Fourier series, plot of the diffraction spectrum observed when the phase shift is n-. The small dc peak shown may come either from the dc term in Eq. Figures 3 b and 3 c show results obtained under the same conditions as Figure 3 a , but with the open to closed ratio of the grating being and , respectively.
This is important from a practical point of view, since a thresholded JTPS more resembles a grating with an open to closed ratio which deviates from a Ronchi grating. Thus the output correlation peak, at most, will have the structure shown in Figure 3 b or Figure 3 c instead of the structure shown in Figure 3 a.
Once the phase shift parameters are known in terms of the brightness control voltage, polarization direction, and zyxwvuts When this. This pattern is then bin- arized and displayed back on the LCTV.
Figure 4 a shows the binarized JTPS and 4 b shows the correlation output due to the input images shown in Figure 1. I t should be noted that only the k1 diffraction orders are shown.
The analysis zyxwvutsrq shows that, beside a delta spike at the origin, which can be where A is a constant, and JJ. If the scene described by Eq. The Fourier transformed, it can be seen that aside from a pro- intensity of the output correlation peaks depends on the mod- portionality constant, an infinite number of diffraction orders ulation depth of the phase.
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