METHOD AND APPARATUS FOR INCREASING THE INFORMATION TRANSMITTING CAPABILITIES OF IMAGE FORMING SYSTEMS
United States Patent 3650594
A process for increasing the transmitting information possibilities in connection with image-mapping systems, in which the information is transmitted from the object space to the image space by waves. The process is characterized in that The spacial frequencies of the structure to be examined are transformed into the range of smaller spacial frequency by the diffraction of evanesent waves it becomes possible for hitherto inaccessible spacial frequencies to be transformed into the conventional range.
US Patent References:
SAMPLING TECHNIQUES FOR HOLOGRAMS
Collier et al. - June 1970 - 3516721
SPATIAL FREQUENCY REDUCTION IN HOLOGRAPHY
Upatnieks - October 1970 - 3532407
SAMPLING TECHNIQUES FOR HOLOGRAMS
Collier et al. - June 1970 - 3516721
SPATIAL FREQUENCY REDUCTION IN HOLOGRAPHY
Upatnieks - October 1970 - 3532407
Application Number:
05/014477
Publication Date:
03/21/1972
Filing Date:
02/26/1970
View Patent Images:
Export Citation:
Assignee:
Farbenfabriken Bayer Aktiengesellschaft (Leverkusen, DT)
Primary Class:
Other Classes:
359/569
International Classes:
G02B27/56; G03H1/00; G02B27/22; G02B5/18
Field of Search:
350/3.5,162SF
Other References:
Morgenstern et al., J. Opt. Soc'y AM., Vol. 54, No. 10, pp. 1282-1283 (10/1964)..
Primary Examiner:
Schonberg, David
Assistant Examiner:
Sherman, Robert L.
Claims:
I claim
1. A process of improving the information transmitting properties when mapping images by means of waves, comprising the step of
2. A process according to claim 1, and producing the subwaves by total reflection.
3. A process according to claim 1, and producing the subwaves by diffraction of normal waves on a grating having a grating constant smaller than the wavelength of the normal waves.
4. A process according to claim 3, and producing the subwaves on a grating having a phase structure.
5. A process according to claim 3, and producing the sub-waves on a grating having an amplitude structure.
6. Process according to claim 1, and transmitting said homogeneous waves of wave number kb through an optical image forming system having the magnification M, and modulating the homogeneous waves on a carrier frequency ks /M to form a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
7. A process according to claim 6 and modulating the homogeneous waves on the carrier frequency by optical gratings.
8. A process according to claim 6, and modulating the homogeneous waves on the carrier frequency holographically.
9. A process of improving the information transmitting properties when mapping images by means of waves, comprising the step of
10. Process according to claim 9, and transmitting said homogeneous waves of wave number kb through an optical image forming system having the magnification M and modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
11. A process of improving the information transmitting properties when mapping images by means of waves, comprising the step of
12. A process according to claim 11, and transmitting said homogeneous waves of wave number kb through an optical image forming system having the magnification M and modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
13. Apparatus for mapping images of objects having a high spatial frequency spectrum ka, comprising:
14. Apparatus according to claim 13, and means for producing the subwaves by total refraction.
15. Apparatus according to claim 13, and a grating having a grating constant smaller than the wave length of the homogeneous waves associated with the illuminating means for producing the subwaves by diffraction of homogeneous waves.
16. Apparatus according to claim 15, said grating having a phase structure.
17. Apparatus according to claim 15, said grating having an amplitude structure.
18. Apparatus according to claim 13, and an optical image forming system for transmission therethrough of said homogeneous wave of number kb.
19. Apparatus according to claim 18, the optical image forming system having the magnification M, and means for modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
20. Apparatus according to claim 19, and an optical grating for modulating the homogeneous waves on the carrier frequency.
21. Apparatus according to claim 19, and means for modulating the homogeneous waves on the carrier frequency holographically.
22. Apparatus for mapping images of objects having a high spatial frequency spectrum ka, comprising:
23. Apparatus according to claim 22, and an optical image forming system for transmission therethrough of said homogeneous waves of wave number kb.
24. Apparatus according to claim 23, said image forming system having the magnification M, and means for modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
25. Apparatus for mapping images of objects having a high spatial frequency spectrum ka, comprising:
26. Apparatus according to claim 25, and an optical image forming system for transmission therethrough of said homogeneous waves of wave number kb.
27. Apparatus according to claim 26, said image forming system having the magnification M, and means for modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
1. A process of improving the information transmitting properties when mapping images by means of waves, comprising the step of
2. A process according to claim 1, and producing the subwaves by total reflection.
3. A process according to claim 1, and producing the subwaves by diffraction of normal waves on a grating having a grating constant smaller than the wavelength of the normal waves.
4. A process according to claim 3, and producing the subwaves on a grating having a phase structure.
5. A process according to claim 3, and producing the sub-waves on a grating having an amplitude structure.
6. Process according to claim 1, and transmitting said homogeneous waves of wave number kb through an optical image forming system having the magnification M, and modulating the homogeneous waves on a carrier frequency ks /M to form a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
7. A process according to claim 6 and modulating the homogeneous waves on the carrier frequency by optical gratings.
8. A process according to claim 6, and modulating the homogeneous waves on the carrier frequency holographically.
9. A process of improving the information transmitting properties when mapping images by means of waves, comprising the step of
10. Process according to claim 9, and transmitting said homogeneous waves of wave number kb through an optical image forming system having the magnification M and modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
11. A process of improving the information transmitting properties when mapping images by means of waves, comprising the step of
12. A process according to claim 11, and transmitting said homogeneous waves of wave number kb through an optical image forming system having the magnification M and modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
13. Apparatus for mapping images of objects having a high spatial frequency spectrum ka, comprising:
14. Apparatus according to claim 13, and means for producing the subwaves by total refraction.
15. Apparatus according to claim 13, and a grating having a grating constant smaller than the wave length of the homogeneous waves associated with the illuminating means for producing the subwaves by diffraction of homogeneous waves.
16. Apparatus according to claim 15, said grating having a phase structure.
17. Apparatus according to claim 15, said grating having an amplitude structure.
18. Apparatus according to claim 13, and an optical image forming system for transmission therethrough of said homogeneous wave of number kb.
19. Apparatus according to claim 18, the optical image forming system having the magnification M, and means for modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
20. Apparatus according to claim 19, and an optical grating for modulating the homogeneous waves on the carrier frequency.
21. Apparatus according to claim 19, and means for modulating the homogeneous waves on the carrier frequency holographically.
22. Apparatus for mapping images of objects having a high spatial frequency spectrum ka, comprising:
23. Apparatus according to claim 22, and an optical image forming system for transmission therethrough of said homogeneous waves of wave number kb.
24. Apparatus according to claim 23, said image forming system having the magnification M, and means for modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
25. Apparatus for mapping images of objects having a high spatial frequency spectrum ka, comprising:
26. Apparatus according to claim 25, and an optical image forming system for transmission therethrough of said homogeneous waves of wave number kb.
27. Apparatus according to claim 26, said image forming system having the magnification M, and means for modulating the homogeneous waves on a carrier frequency ks /M to receive a final undistorted image, wherein the details of the object according to the high spatial frequency spectrum ka are resolved.
Description:
This invention relates to a process for increasing the possibility of transmitting information in connection with image-mapping systems, in which the information is transmitted from the object space to the image space by waves.
In optical systems employing a conventional image-forming arrangement (optical lens system), the resolving power is limited by diffraction effect. The main limit of the resolving power is of the order of 2/λ , where λ is the wavelength of the radiation being used. Even recent activities have not provided any decisive advances. An increase in the resolving power beyond the value 4/λ is very difficult using conventional procedures (W. Lukosz, Phys. Blatter 24 (1968) 554).
Now a type of wave form exists the wavelengths λ s of which is smaller than λ n , where λ n is the wavelength of waves of the same frequency in the particular medium under consideration (refractive index n). These waves are so-called surface waves, also often known as inhomogeneous or evanescent waves. Since the smaller wavelength of these waves is essential for the following, they are designated briefly as "sub-waves." In contrast thereto, waves which are not evanescent are designated herein as "normal" waves.
Sub-waves are formed, for example, when total reflection occurs at the boundary surface of two media 1 and 2 with refractive indices n 1 and n 2 , where n 1 is to be greater than n 2 . When the incidence angle φ 1 of a plane wave in the medium 1 is larger than the critical angle of the total reflection φ gr (sin φ gr = n 2 /n 1 ), a wave is developed in the optically thinner medium 2 in the vicinity of the boundary surface, said wave progressing along the boundary surface and being strongly damped perpendicularly of the latter. The wavelength of this sub-wave is λ s = λ 1 /sinφ 1 , where λ 1 is the wavelength of progressing waves in the medium 1. It is thus apparent that the wavelength at the critical angle φ gr of this wave is equal to λ 2 . With increasing incidence angle φ 1 , the wavelength becomes smaller and finally, with grazing incidence, λ s =λ 1 , i.e., is equal to the wavelength in the denser medium 1. Subwaves of very much smaller wavelength can for example be produced by passing light perpendicular through a grating, perhaps with sinusoidal amplitude transmissivity and having a grating constant a, which is small compared with the wavelength of the radiation. Sub-waves are then formed, which progress in the plane of the grating and are strongly damped perpendicularly of the said plane. The wavelength of these sub-waves is equal to the grating constant a of the irradiated grating. An object of this invention is to develop a process which permits the possibility of transmitting information to be increased when forming images by means of waves. By image formations, there are to be understood here not only geometrically similar image formations. In particular, optical systems are to be found, the resolving powers of which exceed the limits initially indicated.
In the present invention, by the diffraction of sub-waves, the spatial or local frequencies of the structure to be examined, which frequencies are of the order of size of the reciprocal sub-wave length, are transformed into a range of smaller spatial frequency.
FIGS. 1a, 1b, and 1c are frequency spectra for, respectively, an object spatial frequency, the transformed spatial frequency of the object, and the transformed and magnified spatial frequency of the object;
FIG. 2 and FIG. 3 are diagrammatic showings of embodiments of the invention; and
FIG. 4 shows a reconstruction of a double hologram containing positive and negative diffraction orders produced by the method of FIG. 3.
In the following, a structure, the dimensions of which are smaller than the wavelength of the radiation being used, is briefly designated as "sub-structure" relative to this radiation. It was found that by diffraction of a sub-wave on a sub-structure, normal waves are once again obtained. It is of particular importance that a transformation of the spatial frequencies occurs here. By way of example, if a one-dimensional grating (grating constant a, spatial frequency k a =1/a) is irradiated with a sub-wave of the wavelength λ s , i.e., of the wave number k s =1/λ s , a diffraction spectrum is formed with spatial frequencies k b =mk a -k s (m=0, ±1, ±2, ...).
By diffraction of sub-waves, it thus becomes possible for hitherto inaccessible local frequencies k a to be transformed into the conventional range, when │k b │≤│k n │.
For this purpose, the wave number of the sub-wave must be suitably chosen: │mk a -k s │<│k n │. A conventional image-forming system (e.g., a lens) consequently receives the same light distribution as would be caused by a grating with a grating constant b=1/k b with normal irradiation with the wavelength λ. In order to produce an image similar to the object, however, a multiplicative transformation of the type k b x =k a /M is necessary; M is the magnification. Let us initially assume that the essential information of an object is contained in a spatial frequency spectrum of width 2k n (see FIG. 1). It is then immediately to be indicated in the spatial frequency space how k b x is obtained from k b .
k b x =(k b /M)±(K s /M)
It is thus necessary to irradiate the structure k a with sub-waves; the diffracted progressing waves are used for producing an image which is magnified M times ; by modulation to a carrier spatial frequency k s /M by known methods, there is finally formed an image of the structure which is magnified M times, but in which the details corresponding to the spatial frequencies k a are resolved.
The use and diffraction of sub-waves thus offers the following advantages as regards increasing resolving power: (1) the shorter wavelength of the sub-waves is equivalent, as regards the resolution to be produced, to an irradiation with shorter wavelengths (e.g., short-wave ultraviolet or X-rays) which usually are difficult to handle and for which no satisfactory image-forming systems exist.
(2) The homogeneous waves which form due to the diffraction of the sub-waves on the sub-structure and which have the normal wavelength make possible the further processing with the highly developed means (lenses, etc.) of conventional optical systems.
Since the decisive physical value of a wave is the frequency, the properties of the sub-structure, which are important for the wavelength λ and λ n , respectively, are now produced with a resolution which corresponds to a wavelength λ s .
Two methods exist for carrying the process into effect in practice:
1. A sub-wave with the wave number k s is produced on a generator grating with grating constant s, for example, by diffraction of a progressing wave, which is preferably produced with a laser. Disposed in immediate contact with the grating is the structure k a to be examined. With a conventional optical system, e.g., a microscope objective, an image of the structure, magnified M times, is produced. This is transformed into the final image k b x .
2. The sequence indicated above can also be reversed: instead of a generator grating for producing the sub-waves, an analyzer grating k s is used for analyzing the sub-waves with the wave numbers k a which are formed by diffraction of a normal wave on the structure k a to be investigated.
An arrangement for carrying out the process mentioned under (1), which enables the individual steps to be clearly recognized, is shown in FIG. 2: a laser beam 1 falls on a generator grating 2 and produces thereon sub-waves of the wave number k s . These are diffracted by the object structure 3 (spatial frequency k a ) and produce normal waves of wave number k b . A lens 4 produces in its focal plane 5 the Fourier spectrum of k b and, in the image plane 6, an image of the structure k a which is distorted and magnified M times and corresponds to the local frequency spectrum k b . By a lens 7, the local frequency spectrum corresponding to this magnified structure is produced in the plane 8. By a diaphragm 9, the zero diffraction order corresponding to the light passing through without diffraction and the negative local frequencies are masked out. A displaced zero order 13 is introduced by way of a prism 11 and a lens 12 at the angle φ(sinφ = k s /M. For the adaption of amplitude and phase (of this zero order), absorption plates and phase plates can be introduced into the side path of rays.
A lens 10 produces in its rear focal plane an image of the structure which is magnified M times and which is comparable as regards its quality to an image which is obtained with oblique illumination with a conventional microscope, since here, as with the microscope, only the zero diffraction order and a first diffraction order contribute to the image.
An improvement in the image quality by utilizing the positive and the negative diffraction orders can be produced, for example, by holographic methods. An example of this is shown in FIG. 3, which corresponds largely to the arrangement according to FIG. 2. The hologram is formed on a photographic plate 15 by superimposition of the first diffraction order and the displaced zero order with the coherent reference beam 16. If this hologram is reconstructed with the arrangement according to FIG. 4, then there is obtained in the image plane 14 of a lens 17, the same image as with direct observation in the arrangement according to FIG. 2. However, holography offers the possibility of several wave fields, which have been exposed successively, to be coherently superimposed simultaneously. Thus, it is possible on the same photographic plate 15 to expose a second hologram, with which, however, the diaphragm 9 is now so arranged that only the negative first order contributes to the image. The prism 11 and lens 12 are so altered that the zero order is now incident from above at the same angle φ as previously from below. The incidence angle of the reference beam is simultaneously altered so that the angle between reference beam and zero order is the same with both exposures. With the reconstruction of this double hologram in the arrangement according to FIG. 4 with the reconstruction beam 18, there is obtained an image of the structure which now contains the full information over the local frequency range k a . If the displaced zero order is omitted with both exposures, the reconstruction provides a dark field image of the object structure.
The generator or analyzer grating, the grating constant of which is substantially smaller than the wavelength of visible light, can for example be produced by electron-optical methods (R. Speidel Optik 23 (1965) page 125) as amplitude or phase gratings.
With the process according to the invention, and more especially by means of the arrangements described herein, it is possible to produce a resolving power which goes far beyond the resolution limit given by the Abbe theory. In particular, it is also possible to resolve structures which are substantially smaller than λ/4. (λ = wavelength of the light used for forming the image). As regards the resolving power, the objective 4 acts as if the short-wave light of the wavelength of the sub-wave had been used for forming the image.
The process according to the invention can also be transferred to the image formation of two-dimensional structures. Corresponding cross-gratings are then used as gratings.
Using the process according to the invention, it is also possible to form images of and to resolve objects with greater spatial frequency spectrum, for example, when the spatial frequency spectrum of the object only contains substantial contributions in certain intervals. For this purpose, this spectrum has to be split up into bands of width smaller than │k n │. From these bands, it is now possible to produce several bands by sub-waves. For this splitting-up operation, it is for example possible to use successively a plurality of generator and analyzer gratings for sub-waves of different wavelength. The local frequency bands thus obtained are then composed in the image space by known methods (W. Lukosz, Phys. Blatter 24 (1968), 554), to the resultant total image. In this case, the use of holographic methods, in a manner similar to that used for composing the two frequency-shifted spectra, were particularly desirable, since they do in fact permit the simultaneous superimposition of several wave fields taken successively in time.
According to one form of the invention, the information contained in the sub-waves concerning the object is first of all recorded holographically and thereafter is transferred by diffraction of sub-waves on the hologram structure to normal waves.
Amplitude structures and also phase structures are suitable as sub-structures. On account of the coherence of its radiation and its high spectral radiation intensity, a laser is very suitable as a radiation source in the optical field.
The process described is advantageously used in the optical wavelength range (ultraviolet, visible, infra-red). However, it can also be used for electromagnetic waves of other wavelengths, or for radiations of a different nature, which can be presented as waves (for example, electrons, sonic waves or ultra-sonic waves). One particular case where it can be used is, for example, X-ray structure analysis.
In optical systems employing a conventional image-forming arrangement (optical lens system), the resolving power is limited by diffraction effect. The main limit of the resolving power is of the order of 2/λ , where λ is the wavelength of the radiation being used. Even recent activities have not provided any decisive advances. An increase in the resolving power beyond the value 4/λ is very difficult using conventional procedures (W. Lukosz, Phys. Blatter 24 (1968) 554).
Now a type of wave form exists the wavelengths λ s of which is smaller than λ n , where λ n is the wavelength of waves of the same frequency in the particular medium under consideration (refractive index n). These waves are so-called surface waves, also often known as inhomogeneous or evanescent waves. Since the smaller wavelength of these waves is essential for the following, they are designated briefly as "sub-waves." In contrast thereto, waves which are not evanescent are designated herein as "normal" waves.
Sub-waves are formed, for example, when total reflection occurs at the boundary surface of two media 1 and 2 with refractive indices n 1 and n 2 , where n 1 is to be greater than n 2 . When the incidence angle φ 1 of a plane wave in the medium 1 is larger than the critical angle of the total reflection φ gr (sin φ gr = n 2 /n 1 ), a wave is developed in the optically thinner medium 2 in the vicinity of the boundary surface, said wave progressing along the boundary surface and being strongly damped perpendicularly of the latter. The wavelength of this sub-wave is λ s = λ 1 /sinφ 1 , where λ 1 is the wavelength of progressing waves in the medium 1. It is thus apparent that the wavelength at the critical angle φ gr of this wave is equal to λ 2 . With increasing incidence angle φ 1 , the wavelength becomes smaller and finally, with grazing incidence, λ s =λ 1 , i.e., is equal to the wavelength in the denser medium 1. Subwaves of very much smaller wavelength can for example be produced by passing light perpendicular through a grating, perhaps with sinusoidal amplitude transmissivity and having a grating constant a, which is small compared with the wavelength of the radiation. Sub-waves are then formed, which progress in the plane of the grating and are strongly damped perpendicularly of the said plane. The wavelength of these sub-waves is equal to the grating constant a of the irradiated grating. An object of this invention is to develop a process which permits the possibility of transmitting information to be increased when forming images by means of waves. By image formations, there are to be understood here not only geometrically similar image formations. In particular, optical systems are to be found, the resolving powers of which exceed the limits initially indicated.
In the present invention, by the diffraction of sub-waves, the spatial or local frequencies of the structure to be examined, which frequencies are of the order of size of the reciprocal sub-wave length, are transformed into a range of smaller spatial frequency.
FIGS. 1a, 1b, and 1c are frequency spectra for, respectively, an object spatial frequency, the transformed spatial frequency of the object, and the transformed and magnified spatial frequency of the object;
FIG. 2 and FIG. 3 are diagrammatic showings of embodiments of the invention; and
FIG. 4 shows a reconstruction of a double hologram containing positive and negative diffraction orders produced by the method of FIG. 3.
In the following, a structure, the dimensions of which are smaller than the wavelength of the radiation being used, is briefly designated as "sub-structure" relative to this radiation. It was found that by diffraction of a sub-wave on a sub-structure, normal waves are once again obtained. It is of particular importance that a transformation of the spatial frequencies occurs here. By way of example, if a one-dimensional grating (grating constant a, spatial frequency k a =1/a) is irradiated with a sub-wave of the wavelength λ s , i.e., of the wave number k s =1/λ s , a diffraction spectrum is formed with spatial frequencies k b =mk a -k s (m=0, ±1, ±2, ...).
By diffraction of sub-waves, it thus becomes possible for hitherto inaccessible local frequencies k a to be transformed into the conventional range, when │k b │≤│k n │.
For this purpose, the wave number of the sub-wave must be suitably chosen: │mk a -k s │<│k n │. A conventional image-forming system (e.g., a lens) consequently receives the same light distribution as would be caused by a grating with a grating constant b=1/k b with normal irradiation with the wavelength λ. In order to produce an image similar to the object, however, a multiplicative transformation of the type k b x =k a /M is necessary; M is the magnification. Let us initially assume that the essential information of an object is contained in a spatial frequency spectrum of width 2k n (see FIG. 1). It is then immediately to be indicated in the spatial frequency space how k b x is obtained from k b .
k b x =(k b /M)±(K s /M)
It is thus necessary to irradiate the structure k a with sub-waves; the diffracted progressing waves are used for producing an image which is magnified M times ; by modulation to a carrier spatial frequency k s /M by known methods, there is finally formed an image of the structure which is magnified M times, but in which the details corresponding to the spatial frequencies k a are resolved.
The use and diffraction of sub-waves thus offers the following advantages as regards increasing resolving power: (1) the shorter wavelength of the sub-waves is equivalent, as regards the resolution to be produced, to an irradiation with shorter wavelengths (e.g., short-wave ultraviolet or X-rays) which usually are difficult to handle and for which no satisfactory image-forming systems exist.
(2) The homogeneous waves which form due to the diffraction of the sub-waves on the sub-structure and which have the normal wavelength make possible the further processing with the highly developed means (lenses, etc.) of conventional optical systems.
Since the decisive physical value of a wave is the frequency, the properties of the sub-structure, which are important for the wavelength λ and λ n , respectively, are now produced with a resolution which corresponds to a wavelength λ s .
Two methods exist for carrying the process into effect in practice:
1. A sub-wave with the wave number k s is produced on a generator grating with grating constant s, for example, by diffraction of a progressing wave, which is preferably produced with a laser. Disposed in immediate contact with the grating is the structure k a to be examined. With a conventional optical system, e.g., a microscope objective, an image of the structure, magnified M times, is produced. This is transformed into the final image k b x .
2. The sequence indicated above can also be reversed: instead of a generator grating for producing the sub-waves, an analyzer grating k s is used for analyzing the sub-waves with the wave numbers k a which are formed by diffraction of a normal wave on the structure k a to be investigated.
An arrangement for carrying out the process mentioned under (1), which enables the individual steps to be clearly recognized, is shown in FIG. 2: a laser beam 1 falls on a generator grating 2 and produces thereon sub-waves of the wave number k s . These are diffracted by the object structure 3 (spatial frequency k a ) and produce normal waves of wave number k b . A lens 4 produces in its focal plane 5 the Fourier spectrum of k b and, in the image plane 6, an image of the structure k a which is distorted and magnified M times and corresponds to the local frequency spectrum k b . By a lens 7, the local frequency spectrum corresponding to this magnified structure is produced in the plane 8. By a diaphragm 9, the zero diffraction order corresponding to the light passing through without diffraction and the negative local frequencies are masked out. A displaced zero order 13 is introduced by way of a prism 11 and a lens 12 at the angle φ(sinφ = k s /M. For the adaption of amplitude and phase (of this zero order), absorption plates and phase plates can be introduced into the side path of rays.
A lens 10 produces in its rear focal plane an image of the structure which is magnified M times and which is comparable as regards its quality to an image which is obtained with oblique illumination with a conventional microscope, since here, as with the microscope, only the zero diffraction order and a first diffraction order contribute to the image.
An improvement in the image quality by utilizing the positive and the negative diffraction orders can be produced, for example, by holographic methods. An example of this is shown in FIG. 3, which corresponds largely to the arrangement according to FIG. 2. The hologram is formed on a photographic plate 15 by superimposition of the first diffraction order and the displaced zero order with the coherent reference beam 16. If this hologram is reconstructed with the arrangement according to FIG. 4, then there is obtained in the image plane 14 of a lens 17, the same image as with direct observation in the arrangement according to FIG. 2. However, holography offers the possibility of several wave fields, which have been exposed successively, to be coherently superimposed simultaneously. Thus, it is possible on the same photographic plate 15 to expose a second hologram, with which, however, the diaphragm 9 is now so arranged that only the negative first order contributes to the image. The prism 11 and lens 12 are so altered that the zero order is now incident from above at the same angle φ as previously from below. The incidence angle of the reference beam is simultaneously altered so that the angle between reference beam and zero order is the same with both exposures. With the reconstruction of this double hologram in the arrangement according to FIG. 4 with the reconstruction beam 18, there is obtained an image of the structure which now contains the full information over the local frequency range k a . If the displaced zero order is omitted with both exposures, the reconstruction provides a dark field image of the object structure.
The generator or analyzer grating, the grating constant of which is substantially smaller than the wavelength of visible light, can for example be produced by electron-optical methods (R. Speidel Optik 23 (1965) page 125) as amplitude or phase gratings.
With the process according to the invention, and more especially by means of the arrangements described herein, it is possible to produce a resolving power which goes far beyond the resolution limit given by the Abbe theory. In particular, it is also possible to resolve structures which are substantially smaller than λ/4. (λ = wavelength of the light used for forming the image). As regards the resolving power, the objective 4 acts as if the short-wave light of the wavelength of the sub-wave had been used for forming the image.
The process according to the invention can also be transferred to the image formation of two-dimensional structures. Corresponding cross-gratings are then used as gratings.
Using the process according to the invention, it is also possible to form images of and to resolve objects with greater spatial frequency spectrum, for example, when the spatial frequency spectrum of the object only contains substantial contributions in certain intervals. For this purpose, this spectrum has to be split up into bands of width smaller than │k n │. From these bands, it is now possible to produce several bands by sub-waves. For this splitting-up operation, it is for example possible to use successively a plurality of generator and analyzer gratings for sub-waves of different wavelength. The local frequency bands thus obtained are then composed in the image space by known methods (W. Lukosz, Phys. Blatter 24 (1968), 554), to the resultant total image. In this case, the use of holographic methods, in a manner similar to that used for composing the two frequency-shifted spectra, were particularly desirable, since they do in fact permit the simultaneous superimposition of several wave fields taken successively in time.
According to one form of the invention, the information contained in the sub-waves concerning the object is first of all recorded holographically and thereafter is transferred by diffraction of sub-waves on the hologram structure to normal waves.
Amplitude structures and also phase structures are suitable as sub-structures. On account of the coherence of its radiation and its high spectral radiation intensity, a laser is very suitable as a radiation source in the optical field.
The process described is advantageously used in the optical wavelength range (ultraviolet, visible, infra-red). However, it can also be used for electromagnetic waves of other wavelengths, or for radiations of a different nature, which can be presented as waves (for example, electrons, sonic waves or ultra-sonic waves). One particular case where it can be used is, for example, X-ray structure analysis.