GB2065910A

GB2065910A - Method of Manufacturing Inverse Filters by Holographic Techniques

Info

Publication number: GB2065910A
Application number: GB7943088A
Authority: GB
Original assignee: Philips Gloeilampenfabrieken NV
Current assignee: Koninklijke Philips NV
Priority date: 1979-12-14
Filing date: 1979-12-14
Publication date: 1981-07-01
Also published as: GB2065910B

Abstract

An inverse optical filter (8a) for location in the Fourier plane of a lens (L2) for filtering an image of an object (4a), is manufactured by using a single exposure plate having a logarithmic exposure characteristic and modifying the exposure and/or the reference and object wave intensities so that the effect of a combined hologram and amplitude filter is formed after development. A reference object (4) is illuminated with parallel coherent light from a laser (1) via a pinhole diaphragm (2) and a lens (3). A lens (5) effects a Fourier transformation of the object wave O in the plane of a logarithmic recording medium (8). A parallel reference beam R can also be directed at the medium (8). Three embodiments are disclosed:- 1. A single holographic exposure in which the intensity IR of a coherent reference wave R is small compared with the intensity IO of the object wave O. 2. A normal holographic exposure with a coherent reference wave in which IR>IO followed by a further exposure to the object wave alone using a value IO greater than the value IR for the first exposure. 3. A single holographic exposure in which IR??????O, and during which the reference wave is made only partially coherent by passage through a rotating frosted glass plate (9). A composite of plural perspective images of a three-dimensional object, may be decoded by the filter (Figures 1 and 2). <IMAGE>

Description

SPECIFICATION Method of Manufacturing Inverse Filters by Holographic Techniques The invention relates to a method of manufacturing inverse fillers by holographic techniques.

It is generally known that in principle it is possible to enhance an image or to decode an encoded image by subsequent inverse optical filtering in the Fourier plane of a lens, see for example "Industrial Photography", 1 9 May 1970, pages 26 and further. However, currently the optical methods of inverse filtering are not frequently utilized, because the manufacture of such filters is intricate and time-consuming. In addition, the linear recording characteristic of the photographic material normally has a greatly limited dynamic range.If instead of this linearity requirement a specific non-linearity requirement is adopted, i.e. that the resulting amplitude transmittance of the material is proportional to the logarithm of the illumination, this would simplify manufacture of the inverse filter, but this does not suffice if the recording conditions are not adapted to this logarithmic non-linearity.

IEEE Spectrum, Voi. 9, No. 12, 1972, page 34, Fig. 7 describes a method of manufacturing an inverse filter in more detail. The light distribution required for the manufacture of such a filter is obtained by means of a difficult photographic process. An amplitude filter to be made for this purpose comprises two photographic plates, which must be manufactured after each other.

When they are reinserted into the radiation path, they should be adjusted to each other and to the light distribution to be obtained. This poses an adjustment problem. Manufacture of the inverse filter in the first Fourier plane is not possible, because strictly speaking exactly that light distribution should be used for manufacturing the filter, which after leaving the second photographic plate N2 in Fig. 7 is produced directly behind the base. For this reason a second Fourier arrangement is required, which produces said light distribution in the second Fourier plane and it is not until then that the inverse filter can be manufactured by known holographic techniques.

It is the object of the invention to provide a simplified manufacturing method of the type, mentioned in the preamble, by means of which inverse filters in a wide dynamic range can be obtained.

This object is achieved in that for the filter hologram a recording material with a logarithmic characteristic is employed and for the illumination a reference/object-wave intensity ratio is selected which is not unity.

This ensures that the manufacture of a twocomponent amplitude filter as well as an additional second Fourier arrangement may be dispensed with and thus the associated adjustment problem is eliminated. On the contrary, the logarithmic recording of the amplitude filter and of the hologram required for the inverse filter is effected in the first Fourier plane on one and the same photographic plate at the same location. All inverse filters not manufactured in accordance with the inventive method, however, require a second plate/amplitude filter associated with a second Fourier arrangement or at least comprise a sandwhich of amplitude filters and hologram.

If during the manufacture of the filter only one holographic recording is used, it is advantageous in the case of coherent radiation to select the intensity of the reference wave lower than the intensity of the object wave.

It is also possible to make the filter hologram by double illumination, a first illumination being effected with highly coherent light and with an intensity of the reference wave which is higher than that of the object wave, and a second illumination (post-illumination) with the object wave only, the intensity of the object wave being higher than the intensity of the illumination with reference wave.

Filter holograms can also be obtained with semi-coherent light, the intensity of the reference beam being high and its degree of coherence being low.

It is essential that the illumination is adapted to the photographic material in such a way that only the logarithmic portion of the characteristic of the material is used. As the illumination is greatly influenced by the object beam, the illumination cannot always be adapted over the entire recording area. In those cases in which the object wave does not exhibit excessive fluctuations, but the object spectrum is comparatively uniform, the invention is of particularly great advantage.

Such a special case occurs in the case of imaging with encoded sources, as for example described in German Patent Application P 24 14 322.4. A superposition image produced by a plurality of sources is subsequently processed in order to obtain a decoded object.

The decoding in the form of an autocorrelation only yields an approximated reconstruction of the object, whilst by inverse filtering the object is reconstructed in an ideal manner. The objectwave functions in this case are so low and spatially distributed in such a way that inverse filters manufactured in accordance with the novel method are particularly suitable for decoding.

The invention will be described in more detail with reference to the drawing. In the drawing; Figure 1 shows an arrangement for recording the holographic filter, Figure 2 shows an arrangement for filtering an image, Figure 3 represents the "iransmittance/illumination curve of a photographic material as a function of the logarithmic illumination.

In accordance with Figure 1 the light is produced by a laser 1 and is spatially filtered by means of a pinhole diaphragm 2. Lens 3, which is situated at a distance equal to the focal length f from the pinhole diaphragm 2, converts the spherical wave into a plane wave and illuminates the object 4, which is also situated at a distance f from lens 3.

The lens 5 effects a Fourier transformation of the object wave 0 in the plane of the holographic recording material 8 with a logarithmic recording characteristic (Fig. 3).

The reference wave R, which is also generated by the laser 1, is spatially filtered by the pinhole diaphragm 6, the resulting spherical wave being converted into a plane wave by means of the lens 7.

The reference wave R and the object wave 0 illuminate the recording material. A rotating ground-glass plate 9 is inserted into the reference radiation path, if semi-coherent light is used. After development of the recording material 8 the inverse filter now obtained can be used as shown in Fig. 2. The object 4a which is to be filtered, is optically Fourier-transformed. A wave illuminates, the inverse filter 8a. The wave emanating from the filter is Fourier-transformed with the lens 11 as a result of which the filtered object 10 is obtained. Fig. 3 shows a characteristic for a recording material used for manufacture of inverse filters. Of the typical photographic emulsions used for holographic purposes the linear range is employed and the dynamic range is approximately a factor 4, whilst on the logarithmic characteristic the dynamic range is a factor 50.

The illumination for the holographic recording is then (1) E=ç[1 +a2 9 2a cos 0], where 9 is the reference-wave illumination a the vaiue of the object-wave-to reference-wave ratio, and 0 the phase angle of the object and reference wave.

It is known that the periodicity of the angle 0 may be used to describe the amplitude transmittance of the hologram as a Fourier series, i.e.

in which

As the reference phase comprises a carrier frequency, each term of this Fourier series will correspond to a diffraction order of the hologram.

The -1 diffraction order is selected as filter order, so that the effective filter transmittance is given by (4) 7=C~, (a,gD) e~itn where on is the phase of the object wave.

For a logarithmic non-linearity (5) T(E)=T0-T1 In (E), where T0,T1 are constants, a corresponding Fourier series Cm can be derived which corresponds to an inverse filter hologram which has been illuminated once. In order to satisfy this condition, a reference wave is required during the illumination of the hologram, whose intensity is low relative to that of the object wave. This reference/object wave ratio is exactly the opposite of that in the case of the formation of hologram with highly coherent light in accordance with prior methods.

However, when the hologram is illuminated twice in succession, first with an object-toreference wave ratio as is customary for the formation of optimum holograms and subsequently post-illuminated with the object wave, the total illumination will become (6) E=[1 +(1 +b)a2+3a cos Oj where b represents a constant which is proportional to the post-illumination.

If a 1, and (1 +b) a1,2 the filter function will become

(object wave)

(object wave) because the reference wave; and b are constants.

Accordingly, if the holographic plate is illuminated twice in succession, once with a highintensity reference beam, i.e. with an object-toreference wave ratio as is customary for the manufacture of holograms, and once without reference wave, the object illumination then being intense in comparison with the illumination with the reference beam, this also yields an inverse filter.

It is alternatively possible to manufacture a filter with semicoherent light, i.e. the reference beam is only spatially semicoherent relative to the object beam. Such a semicoherence can be obtained by inserting a rotating frosted-glass plate in the path of the reference beam instead of the pinhole diaphragm 6 in Fig. 1. If the hologram is then illuminated with semicoherent light, the reference beam having high intensity and low degree of coherence, this also yields an inverse filter.

The arrangement represented in Fig. 2 may for example also be employed as a device for decoding superposition images of a threedimensional object (not shown), which are recorded from a plurality of radiation source positions and from different perspectives. A superposition image 4a, comprising a plurality of superimposed perspective images, is then arranged between the lenses L1 and L2 and is traversed by the parallel beam P. The filter hologram 8a (inverse filter) located in the Fourier plane of the lens L2 then serves for decoding the superposition image 4a or for reconstructing layer images of the object, if the filter hologram is observed via lens 11. For this purpose the coordinates of the uniform distribution of the radiation source positions are then stored in the filter hologram 8a at a reduced scale. Storage may be realized with the aid of the arrangement shown in Fig. 1, the object 4 being replaced by a pinhole camera recording of the radiation sources (compare DE-PS 24 14 322).

Claims

1. A method of manufacturing inverse filters by holographic techniques, characterized in that for the filter hologram a recording material with a logarithmic characteristic is employed and for the illumination a reference/object-wave intensity ratio is selected which is not unity.

2. A method as claimed in Claim 1, characterized in that the filter is manufactured by holographic recording in such a way that in the case of coherent radiation the reference wave has a lower intensity than the object wave.

3. A method as claimed in Claim 1, characterized in that the filter hologram is made by double illumination in such way that illumination is effected with highly coherent light and with a reference wave which has a high intensity relative to the object wave, and subsequently a second illumination (postillumination) is effected with the object wave only, the intensity of said object wave being higher than that of the reference wave illumination.

4. A method as claimed in Claim 1, characterized in that a hologram is made with semicoherent light, the reference beam having a high intensity and a low degree of coherence.

5. A method as claimed in Claim 4, characterized in that the low degree of coherence of the reference beam is obtained continuously be extending the optical pathlength relative to the object wave.

6. A method as claimed in Claim 4, characterized in that the reference wave is filtered by a pinhole diaphragm.

7. A method as claimed in Claim 4, characterized in that a rotating frosted-glass plate is arranged in the radiation path of the reference wave.

8. A filter hologram formed in accordance with any one of the preceding Claims, characterized in that it comprises a single layer of a holographic recording material with a logarithmic characteristic.

9. A device for decoding superposition images (4a) of a three-dimensional object, which is illuminated from a plurality of radiation-source positions from different perspectives for recording the superposition images, comprising a radiation source (1) for illuminating the superposition images, an optical imaging system for imaging the superposition images in an imaging plane, in which a hologram (8a) is arranged, in which the coordinates of the radiation source positions are stored by means of a pinhole camera recording of the radiation sources, and a further optical imaging system (11) arranged behind the hologram for observing the layer images of the object, characterized in that the hologram (8a) is a filter hologram as claimed in Claim 8.

10. A method of manufacturing inverse filters by holographic techniques as claimed in Claim 1, substantially as herein described with reference to the accompanying drawings.