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Holography through fog. A new version
Volume 26, number 3
OPTICS COMMUNICATIONS
September 1978
HOLOGRAPHY THROUGH FOG. A NEW VERSION A.W. LOHMANN and H. SCHMALFUSS
Physikalisches Institut, 8520 Erlangen, West Germany Received 31 May 1978 Seeing through fog is better with holography than with ordinary photography or human vision. This has to do with the Doppler effect, which is imparted on the light that is scattered by moving fog droplets. Experiments of this type are known since about ten years. So far, these experiments were always performed with off-axis holography, while we now propose to use on-axis holography. The new approach is better matched to the capabilities of the electronic components that are needed for hologram reconstruction in real-time. Advantages in resolution and dynamic range are predicted and verified experimentally. 1. Introduction
2. Explanation of on-axis holography in real-time
Fog droplets or any other scattering particles deteriorate the vision. This deterioration can be avoided, if holography is employed for viewing through the fog. This favourable aspect of holography is caused by the Doppler effect, which is imparted upon the scattered light, if the scattering particles are moving, as they usually are. About ten years ago, Sputz [1] and Stetson [2] recognized the advantage of holography for viewing through fog. This was verified several times [3,4], more recently also in real-time by using TV technology for decoding the hologram instantaneously [5 ]. It was recognized that the resolution can be doubled, sometimes [6], and that the coherence requirements are not very severe, which is desirable for any practical applications [71. So far, holography through fog was always performed with off-axis arrangements. Here, we will show, that also on-axis holography is suitable for viewing through fog. On-axis holography yields better resolution and better dynamic range, two features that are only of marginal quality, when TV technology is involved, especially in connection with off-axis holography. Our plan is to explain the new concept, to show some experimental results, and to compare on-axis with off-axis holography, when combined with TV.
The object Uo(x ) is imaged into the target plane of the TV camera. There, also the scattered light Us(x, t) arrives, fluctuating in amplitude and phase due to the moving fog. The reference wave R n is co-planar to the object wave. The phase of the reference wave can be modified by the phase shifter P. Complex amplitudes, instant intensities and exposures are listed in eq. (1), the set-up is sketched in fig. 1
318
\
tIGHT
IS
OBJ[CI
\
\
~P Fig. 1. Setup for image holography. BS: beamsplitter; M:mirror; P: phase shifter; L: imaging lens; TV: TV camera; EL: electric devices; M: monitor.
Volume 26, number 3
OPTICS COMMUNICATIONS
Uo(x) + Us(x, t) + R,, = U,,(x, O, n = 1,2;
R 1 = +1,
(1)
R 2 = -1, T
In(X,t)=lUn(X,t)l 2,
En(x)=~f In(x, Odt. o
The temporal average of the scattered amplitude is zero under suitable conditions [3], but not the average scatter intensity eq. (2). The time T is the integration time of the TV camera. T T Us(x,t) dt~O; l f lUsl2dt=S; [ U o [ 2 = I o . 0 0 (2) By combining eq. (1) and eq. (2) we obtain:
E l ( x ) = Io(x) + s + 1 + Uo(x) + Ca(x), u 2 ( x ) = Io(x) + s + 1 - Uo(x) - Ua(x).
(3)
The exposures E 1 and E 2 are picked up by the TV camera, for example as sequential frames. The first frame signal E 1 is stored in EL (fig. 1); the second frame signal is subtracted electronically. Hence, one gets:
meters was used recently by Pappu and Rao [8] for the suppression of the background terms in on-line holography. Those authors performed the subtraction in a secondary interferometer. Now we assume, we obtained electronically the difference E 1 (x) - E 2 (x). Obviously, this signal may become negative if the object phase lies around 180 °. The TV monitor cannot display negative brightness, of course. It acts like an one-way rectifier, showing darkness, whenever the amplitude signal goes negative. Sometimes, these dark spots will be tolerable, for example if the object is rough and hence the phase wildly fluctuating. Then, we are used to see a speckled holographic image anyway. If however, the object phase is a slowly varying function, we may suppress its impact by a quadrature approach. In other words, we take four exposures with suitable reference phases, as expressed in eq. (5): R 1 =+1,
R 2 =-1,
R 3 =+i,
E1-E2=4IUo Icos~o=Ec,
R 4 =-i;
E 3 - E 4 = 4 [ U 0 l s i n t p = E s,
f 2 + E 2 = 161Uo(x)l 2.
(5)
Already three exposures are enough:
El(X) - E2(x) = 2U0(x ) + 2U~0(x)
RI=+I, = 41U0(x)l cos ~0(x).
September 1978
R 2 = e x p ( + 2 • i / 3 ),
R3=exp(-21ri/3);
(4)
Apparently, this difference is free of all undesirable terms such as the average scatter intensity S. The main goal is achieved now. Two problems will be discussed now in some detail, the method of obtaining the difference, and the influence of the object phase ~0. So far, we suggested to record E 1 and E 2 sequentially. That requires a store for the TV signal and a phase shifter for changing the reference wave from +1 to - 1 between exposures. The interferometer (fig. 1) has to remain stable from one exposure to the other. The stability requirement and the need for a TV store are avoided, if two TV cameras are used simultaneously at both exits of the interferometer (fig. 1). Because of conservation of energy, the total output E 1 + E 2 from both exi[s cannot depend on the object phase ~0. Hence, the conservation law guarantees us, that the exposures from the two exits will be of the form shown in eq. (3). In other words, the exposure difference will be free from the scatter intensity S and from the two other undesirable terms [1 + I0(x)]. This feature of Mach-Zehnder interfero-
(E 3 - E 2 ) 2 + 3 E 2 = 121U0(x)I 2.
(6)
It is possible to construct interferometers with three exits, yielding El, E 2, E 3 simultaneously.
3. Experimental verification We used essentially the setup shown in fig. 1. The block EL consisted of a TV storage unit (Hughes) and an inverter, that was able to switch E2(x ) into 1 E2(x ). The storage unit itself could not subtract, only add. The first exposure E 1 consisted of an incoherent superposition of a cat and a four times weaker test pattern (fig. 2a). The second exposure was the cat alone. The difference signal on the monitor is shown in fig. 2b. This preliminary experiment without holography served to test the dynamic range and distortion of our electronic components. The result of a holographic experiment with the electronic components as mentioned above is shown in fig. 3b. For comparison, fig. 3a was obtained as an or319
Volume 26, number 3
OPTICS COMMUNICATIONS
September 1978
Fig. 2. Image subtraction test experiment. A) Cat/test chart intensity ratio 4/1. B) (A) minus cat..
Fig. 3. Viewing through fog with TV in real-time. A) ordinary viewing. B) with on-axis holography.
dinary image through the same fog by covering up the reference beam. The fog consisted of a moving piece of soft paper tissue (Kleenex). Apparently, the holographically produced image (fig. 3b) is superior to the ordinary image (fig. 3a). The electronic components available to us were far from optimal for this purpose. Hence, these results should not be considered as showing the limits of the concept.
the object related term [ (201 cos ~p. Then, the exposure difference gets rid of all undesirable terms such as the scatter intensity. In off-axis holography the suppression of the undesirable terms is accomplished in another way. The undesirable terms consist of low spatial frequencies, while the object term contains only high spatial frequencies. The TV scanning converts the spatial frequencies of the hologram into temporal frequencies of electronic nature. A high pass filter suppresses the lower frequencies, leaving only the object term, which is finally displayed on the monitor. The problem with this off-axis approach is that the TV camera usually has a poor transfer function for
4. Comparison with off-axis holography As we have seen, in on-axis holography, we need two hologram exposures with opposite polarities of 320
Volume 26, number 3
OPTICS COMMUNICATIONS
the important higher frequencies. In other words, the dynamic range will suffer. Furthermore, the high pass filter eliminates half of the video frequency band. This corresponds to a reduction o f spatial frequency bandwidth by a factor 1/2. Another undesirable aspect of the high pass filter is its phase transfer characteristics, that tends to be wild close to the transmission edge. Taking all advantages and disadvantages into account, it seems to us that an on-axis setup with a single camera and a fast digital storage device would be the best solution with today's technology.
September 1978
References [1] E. Spitz, C.R. Acad. Sc. Paris 264 (1967) 1449. [2] K.A. Stetson, J. Opt. Soc. Am. 57 (1967) 1060. [3] A.W. Lohmann and C.A. Shuman, Opt. Comm. 7 (1973) 93. [4] D.C. Winter, Appl. Phys. Lett. 22 (1973) 15l. [5] H. Schmalfuss, Opt. Comm. 17 (1976) 245. [6] H. Schmalfuss, Optik 48 (1977) 119. [7] H. Schmalfuss, Coherence requirements for holography through fog, to appear in Optik. [8] S.V. Pappu and S.A. Rao, Pramana (India) 10 (1978) 239.
321
OPTICS COMMUNICATIONS
September 1978
HOLOGRAPHY THROUGH FOG. A NEW VERSION A.W. LOHMANN and H. SCHMALFUSS
Physikalisches Institut, 8520 Erlangen, West Germany Received 31 May 1978 Seeing through fog is better with holography than with ordinary photography or human vision. This has to do with the Doppler effect, which is imparted on the light that is scattered by moving fog droplets. Experiments of this type are known since about ten years. So far, these experiments were always performed with off-axis holography, while we now propose to use on-axis holography. The new approach is better matched to the capabilities of the electronic components that are needed for hologram reconstruction in real-time. Advantages in resolution and dynamic range are predicted and verified experimentally. 1. Introduction
2. Explanation of on-axis holography in real-time
Fog droplets or any other scattering particles deteriorate the vision. This deterioration can be avoided, if holography is employed for viewing through the fog. This favourable aspect of holography is caused by the Doppler effect, which is imparted upon the scattered light, if the scattering particles are moving, as they usually are. About ten years ago, Sputz [1] and Stetson [2] recognized the advantage of holography for viewing through fog. This was verified several times [3,4], more recently also in real-time by using TV technology for decoding the hologram instantaneously [5 ]. It was recognized that the resolution can be doubled, sometimes [6], and that the coherence requirements are not very severe, which is desirable for any practical applications [71. So far, holography through fog was always performed with off-axis arrangements. Here, we will show, that also on-axis holography is suitable for viewing through fog. On-axis holography yields better resolution and better dynamic range, two features that are only of marginal quality, when TV technology is involved, especially in connection with off-axis holography. Our plan is to explain the new concept, to show some experimental results, and to compare on-axis with off-axis holography, when combined with TV.
The object Uo(x ) is imaged into the target plane of the TV camera. There, also the scattered light Us(x, t) arrives, fluctuating in amplitude and phase due to the moving fog. The reference wave R n is co-planar to the object wave. The phase of the reference wave can be modified by the phase shifter P. Complex amplitudes, instant intensities and exposures are listed in eq. (1), the set-up is sketched in fig. 1
318
\
tIGHT
IS
OBJ[CI
\
\
~P Fig. 1. Setup for image holography. BS: beamsplitter; M:mirror; P: phase shifter; L: imaging lens; TV: TV camera; EL: electric devices; M: monitor.
Volume 26, number 3
OPTICS COMMUNICATIONS
Uo(x) + Us(x, t) + R,, = U,,(x, O, n = 1,2;
R 1 = +1,
(1)
R 2 = -1, T
In(X,t)=lUn(X,t)l 2,
En(x)=~f In(x, Odt. o
The temporal average of the scattered amplitude is zero under suitable conditions [3], but not the average scatter intensity eq. (2). The time T is the integration time of the TV camera. T T Us(x,t) dt~O; l f lUsl2dt=S; [ U o [ 2 = I o . 0 0 (2) By combining eq. (1) and eq. (2) we obtain:
E l ( x ) = Io(x) + s + 1 + Uo(x) + Ca(x), u 2 ( x ) = Io(x) + s + 1 - Uo(x) - Ua(x).
(3)
The exposures E 1 and E 2 are picked up by the TV camera, for example as sequential frames. The first frame signal E 1 is stored in EL (fig. 1); the second frame signal is subtracted electronically. Hence, one gets:
meters was used recently by Pappu and Rao [8] for the suppression of the background terms in on-line holography. Those authors performed the subtraction in a secondary interferometer. Now we assume, we obtained electronically the difference E 1 (x) - E 2 (x). Obviously, this signal may become negative if the object phase lies around 180 °. The TV monitor cannot display negative brightness, of course. It acts like an one-way rectifier, showing darkness, whenever the amplitude signal goes negative. Sometimes, these dark spots will be tolerable, for example if the object is rough and hence the phase wildly fluctuating. Then, we are used to see a speckled holographic image anyway. If however, the object phase is a slowly varying function, we may suppress its impact by a quadrature approach. In other words, we take four exposures with suitable reference phases, as expressed in eq. (5): R 1 =+1,
R 2 =-1,
R 3 =+i,
E1-E2=4IUo Icos~o=Ec,
R 4 =-i;
E 3 - E 4 = 4 [ U 0 l s i n t p = E s,
f 2 + E 2 = 161Uo(x)l 2.
(5)
Already three exposures are enough:
El(X) - E2(x) = 2U0(x ) + 2U~0(x)
RI=+I, = 41U0(x)l cos ~0(x).
September 1978
R 2 = e x p ( + 2 • i / 3 ),
R3=exp(-21ri/3);
(4)
Apparently, this difference is free of all undesirable terms such as the average scatter intensity S. The main goal is achieved now. Two problems will be discussed now in some detail, the method of obtaining the difference, and the influence of the object phase ~0. So far, we suggested to record E 1 and E 2 sequentially. That requires a store for the TV signal and a phase shifter for changing the reference wave from +1 to - 1 between exposures. The interferometer (fig. 1) has to remain stable from one exposure to the other. The stability requirement and the need for a TV store are avoided, if two TV cameras are used simultaneously at both exits of the interferometer (fig. 1). Because of conservation of energy, the total output E 1 + E 2 from both exi[s cannot depend on the object phase ~0. Hence, the conservation law guarantees us, that the exposures from the two exits will be of the form shown in eq. (3). In other words, the exposure difference will be free from the scatter intensity S and from the two other undesirable terms [1 + I0(x)]. This feature of Mach-Zehnder interfero-
(E 3 - E 2 ) 2 + 3 E 2 = 121U0(x)I 2.
(6)
It is possible to construct interferometers with three exits, yielding El, E 2, E 3 simultaneously.
3. Experimental verification We used essentially the setup shown in fig. 1. The block EL consisted of a TV storage unit (Hughes) and an inverter, that was able to switch E2(x ) into 1 E2(x ). The storage unit itself could not subtract, only add. The first exposure E 1 consisted of an incoherent superposition of a cat and a four times weaker test pattern (fig. 2a). The second exposure was the cat alone. The difference signal on the monitor is shown in fig. 2b. This preliminary experiment without holography served to test the dynamic range and distortion of our electronic components. The result of a holographic experiment with the electronic components as mentioned above is shown in fig. 3b. For comparison, fig. 3a was obtained as an or319
Volume 26, number 3
OPTICS COMMUNICATIONS
September 1978
Fig. 2. Image subtraction test experiment. A) Cat/test chart intensity ratio 4/1. B) (A) minus cat..
Fig. 3. Viewing through fog with TV in real-time. A) ordinary viewing. B) with on-axis holography.
dinary image through the same fog by covering up the reference beam. The fog consisted of a moving piece of soft paper tissue (Kleenex). Apparently, the holographically produced image (fig. 3b) is superior to the ordinary image (fig. 3a). The electronic components available to us were far from optimal for this purpose. Hence, these results should not be considered as showing the limits of the concept.
the object related term [ (201 cos ~p. Then, the exposure difference gets rid of all undesirable terms such as the scatter intensity. In off-axis holography the suppression of the undesirable terms is accomplished in another way. The undesirable terms consist of low spatial frequencies, while the object term contains only high spatial frequencies. The TV scanning converts the spatial frequencies of the hologram into temporal frequencies of electronic nature. A high pass filter suppresses the lower frequencies, leaving only the object term, which is finally displayed on the monitor. The problem with this off-axis approach is that the TV camera usually has a poor transfer function for
4. Comparison with off-axis holography As we have seen, in on-axis holography, we need two hologram exposures with opposite polarities of 320
Volume 26, number 3
OPTICS COMMUNICATIONS
the important higher frequencies. In other words, the dynamic range will suffer. Furthermore, the high pass filter eliminates half of the video frequency band. This corresponds to a reduction o f spatial frequency bandwidth by a factor 1/2. Another undesirable aspect of the high pass filter is its phase transfer characteristics, that tends to be wild close to the transmission edge. Taking all advantages and disadvantages into account, it seems to us that an on-axis setup with a single camera and a fast digital storage device would be the best solution with today's technology.
September 1978
References [1] E. Spitz, C.R. Acad. Sc. Paris 264 (1967) 1449. [2] K.A. Stetson, J. Opt. Soc. Am. 57 (1967) 1060. [3] A.W. Lohmann and C.A. Shuman, Opt. Comm. 7 (1973) 93. [4] D.C. Winter, Appl. Phys. Lett. 22 (1973) 15l. [5] H. Schmalfuss, Opt. Comm. 17 (1976) 245. [6] H. Schmalfuss, Optik 48 (1977) 119. [7] H. Schmalfuss, Coherence requirements for holography through fog, to appear in Optik. [8] S.V. Pappu and S.A. Rao, Pramana (India) 10 (1978) 239.
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