WO2000062103A1

WO2000062103A1 - Fresnel zone plate comprised entirely of transparent constructive zones

Info

Publication number: WO2000062103A1
Application number: PCT/US1999/012982
Authority: WO
Inventors: Kan Cheng
Original assignee: Kan Cheng
Priority date: 1999-04-14
Filing date: 1999-06-07
Publication date: 2000-10-19
Also published as: AU4430299A

Abstract

The present Fresnel zone plate (20) is comprised of a plate with alternating thin and thick transparent zones. The thin transparent zones (21) are of the same thickness, and the thick transparent zones (22) are of the same thickness. All zones have parallel opposite faces. The thick transparent zones are thicker than the thin transparent zones by a suitable amount to delay incoming destructive waves by an integer of at least zero plus half a wavelength, so that after the waves are passed through the zone plate, waves in all zones are in phase with each other when they reach a focal point (P). Thus, all the zones are transparent constructive zones for passing all incoming radiation to produce twice the amplitude or four times the intensity of a conventional Fresnel zone plate.

Description

TITLE OF THE INVENTION

Fresnel Zone Plate Comprised Entirely of Transparent Constructive Zones

BACKGROUND OF THE INVENTION

1. Field Of The Invention:

This invention relates generally to Fresnel zone plates.

2. Prior Art:

Diffraction is the change in amplitude and phase of waves after passing an obstacle or aperture. Waves that are in phase with each other add together to produce a wave of greater amplitude, whereas waves that are out of phase with each other, i.e., offset by a half a wavelength or Pi (λ/2 = π), cancel out each other. Diffraction is exhibited by all types of waves, including electromagnetic, sound, and water waves. In light waves, diffraction is manifested as light and dark areas, called a diffraction pattern, in the shape of the obstacle.

The two main types of diffraction are Fraunhofer and Fresnel diffraction, which respectively concern parallel and divergent light. In Fig. 1, a Fresnel diffraction pattern 10 is projected on a surface 11 by a point-source light S shining through a circular aperture 12 on a screen 13. Diffraction pattern 10 includes alternating circular light areas 14 and circular dark areas 15. Light areas 14 are constructive zones in which light waves W are in phase with each other. Dark areas 15 are destructive zones in which light wave are out of phase by half a wavelength with respect to the light in the constructive zones, so that they cancel out each other. A Fresnel zone plate is a type of inexpensive lens based on the principles of Fresnel diffraction. As shown in Fig. 2, it is comprised of a flat plate 16 with alternating circular transparent zones 17 and circular dark or opaque zones 18. Transparent zones 17 correspond to constructive zones, and dark zones 18 correspond to destructive zones.

When light from a point source S is passed through a flat transparent plate 16 with a pole O, light waves that pass through pole O travel a path b to a focal point P, and light waves that pass through the outer part of the plate travel a path r to focal point P. Since r > b, there is a phase difference δ between the light waves as follows:

_ 2π . π(a + b) ₂ δ = — (r - b) « — -s λ abλ

As shown in the vibration curve for the Fresnel zone plate in Fig. 3, negative contribution or destructive zones represented by the dashed lines appear periodically between 180 and 360 degrees, i.e., every half wavelength. The destructive zones reduce the total amplitude of the transmitted light. As shown in Fig. 2, when the destructive zones are darkened into dark zones 18, out-of-phase waves are blocked, and only in-phase waves W are passed through transparent zones 17. For a zone plate with a transparent center zone 1 , zones 2, 4, 6, etc. are blocked, as represented by the dashed lines in Fig. 3. The in-phase waves are diffracted by the edges of the zones to focus at point P in Fig. 2, and are combined with each other to increase in amplitude and produce an intense point of light. By putting δ = π (phase difference = half a wavelength) and a = ∞ in the above equation, the Fresnel zone plate is found to have a focal length b as follows:

b = s,7λ,

where s, is the radius of the first boundary between the central zone and the next zone, and λ is the wavelength of the light. Accordingly, the radius s, is as follows:

s, = Vbλ The radii of the boundaries between the transparent and dark zones are chosen so that the phase difference is half a wavelength between adjacent boundaries. For the second zone, δ = 2π, and 2πbλ = πs,². Thus the radius s₂ of the second zone is as follows:

Accordingly, the radii of the boundaries are as follows:

s_n = s, n , where n = 1, 2, 3, 4 ... (consecutive positive integers).

The flat Fresnel zone plate is used as a focusing lens. It is much less expensive than a conventional optical lens with curved surfaces. However, it blocks half the incoming light, so that it only has half the amplitude or a quarter of the intensity as a conventional lens (intensity is proportional to the square of amplitude). Further, the blocked light energy is absorbed by the plate. When the light energy is high enough, the plate may get hot enough to become distorted or damaged.

OBJECTS OF THE INVENTION

Accordingly, objects of the present Fresnel zone plate are: to focus radiation based on the principles of Fresnel diffraction; to be entirely comprised of transparent constructive zones for passing all incoming radiation; to produce twice the amplitude or four times the intensity of a conventional Fresnel zone plate; and to be inexpensive to make.

Further objects of the present invention will become apparent from a consideration of the drawings and ensuing description. BRIEF SUMMARY OF THE INVENTION

The present Fresnel zone plate is comprised of a plate with alternating thin and thick transparent zones. The thin transparent zones are of the same thickness, and the thick transparent zones are of the same thickness. All zones have parallel opposite faces. The thick transparent zones are thicker than the thin transparent zones by a suitable amount to delay incoming destructive waves by an integer of at least zero plus half a wavelength, so that after the waves are passed through the zone plate, waves in all zones are in phase with each other when they reach the focal point. Thus all the zones are transparent constructive zones for passing all incoming radiation to produce twice the amplitude or four times the intensity of a conventional Fresnel zone plate.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

Fig. 1 is a top perspective view of a prior art Fresnel diffraction pattern.

Fig. 2 is a top perspective view of a prior art Fresnel zone plate.

Fig. 3 is a vibration curve of a prior art Fresnel zone plate.

Fig. 4 is a top perspective view of a first embodiment of the present Fresnel zone plate.

Fig. 5 is a vibration curve of the Fresnel zone plate of Fig. 4.

Fig. 6 is a top perspective view of a second embodiment of the present Fresnel zone plate.

Fig. 7 is a vibration curve of the Fresnel zone plate of Fig. 6.

Fig. 8 is a first step in the making of the present Fresnel zone plate.

Fig. 9 is a second step in the making of the present Fresnel zone plate. Fig. 10 is a third step in the making of the present Fresnel zone plate.

Fig. 11 is a fourth step in the making of the present Fresnel zone plate.

Fig. 12 is a top perspective view of a third embodiment of the present Fresnel zone plate.

DRAWING REFERENCE NUMERALS

10. Diffraction Pattern 11. Surface

12. Aperture 13. Screen

14. Light Areas 15. Dark Areas

16. Plate 17. Transparent Zones

18. Dark Zones 20. Plate

21. Thin Transparent Zones 22. Thick Transparent Zones

30. Transparent Plate 31. Transparent Coating

32. Photo Mask 33. Transparent Zones

34. Dark Zones 40. Plate

41. Thin Transparent Zones 42. Thick Transparent Zones b. Focal Length H. Hardening Radiation

W. Waves P. Focal Point

DETAILED DESCRIPTION OF THE INVENTION

Figs. 4-5:

A first embodiment of the present Fresnel zone plate is shown in the top perspective view in Fig. 4. It is comprised of a plate 20 with annular thin transparent zones 21 alternating with annular thick transparent zones 22. Thin transparent zones 21 are all of the same thickness, and have parallel opposite faces. Thick transparent zones 22 are all of the same thickness, and have parallel opposite faces. The central zone is preferably a transparent zone, and has a radius s, as follows:

bλ .

The radii or perpendicular distances s_n between the boundaries of the other zones and the center of the central zone are generally equal to the square roots of consecutive positive integers multiplied by the radius of the central zone s,. The formula is as follows:

s_n = s, n , where n = 1, 2, 3, 4 ... (consecutive positive integers).

The zone plate can be of any diameter and have any number of zones as long as the boundaries are properly proportioned. The zone plate may be made of any suitable material which is transparent to a selected range of electromagnetic radiation, including gamma rays, x-rays, ultraviolet rays, visible light, infrared waves, microwaves, and radio waves. E.g., an acrylic plate is transparent to visible light, whereas a wood plate is transparent to x-rays.

Radiation slows when it is passing through a transparent substance, and resumes its original speed after leaving the transparent substance. Waves W passing through thin transparent zones 21 are slowed by the same amount, so that they remain in phase with each other when they reach focal point P. Waves W passing through thick transparent zones 22 have to travel through more transparent substance, so that they are slowed more relative to the waves passing through thin transparent zones 21. Depending on its refractive index, thick transparent zones 22 are made thicker than thin transparent zones 21 by a suitable amount to delay incoming destructive waves by half a wavelength (λ/2 or π), so that after the waves are passed through zone plate 20, waves in all zones are in phase with each other when they reach focal point P.

Alternatively, a greater delay equal to a positive integer plus half a wavelength may be provided. The equation for the greater delay is: (n + 1/2) λ, where n = 1 , 2, 3 4 ... (consecutive positive integers).

Regardless of the integer used in the equation, the net effect is that the destructive waves are always offset relative to the constructive waves by half a wavelength, so that all waves are in phase with each other when they reach focal point P. The vibration curve for the Fresnel zone plate of Fig. 4 is shown in Fig. 5. For a zone plate with a thin center zone, a 180 degree phase shift is added to even zones 2, 4, 6, etc. Alternatively, the thick and thin zones can be reversed, so that the center zone or zone 1 is a thick zone. For a zone plate with a thick center zone, a 180 degree phase shift is added to odd zones 3, 5, 7, etc.

Thus all zones of the present Fresnel zone plate are transparent constructive zones for passing all incoming radiation to produce twice the amplitude or four times the intensity of a conventional Fresnel zone plate.

Figs. 6-7:

A second embodiment of the present Fresnel zone plate is shown in Fig. 6. ft is the same as the first embodiment shown in Fig. 4, except for radii of the zone boundaries. In this embodiment, the phase difference δ and radius s, for the first zone are as follows:

a ^π ^{δ =} 2 '

The phase difference δ and radius s₂ for the second zone are as follows:

δ _s = - ³ π

2 s₂

⁼ 2 ^{bλ = S}'^ ^'

The phase difference between succeeding zones is half a wavelength or π. Therefore, the radii or perpendicular distances s_n between the boundaries of the zones and the center of the central zone are generally equal to the square roots of consecutive positive odd integers multiplied by the radius of the central zone s,. The formula is as follows:

s_n = s, Vm, where n = 1, 2, 3, 4, ... (consecutive positive integers), and m = 1, 3, 5, 7 (consecutive positive odd integers).

The vibration curve for the Fresnel zone plate of Fig. 6 is shown in Fig. 7. Without the thick zones, the vectors for zones 2, 4, 6, etc. would have been out of phase with the vectors of zones 1, 3, 5, etc., as indicated by the dashed lines (when the center zone or zone 1 is a thin zone). With alternating thick and thin zones, the vectors for zones 2, 4, 6, etc. are shifted 180 degrees to the positions indicated by the solid lines. Therefore, the amplitude increase is the same as for the first embodiment shown in Fig. 4.

Figs. 8-11 :

A preferred method of making the present Fresnel zone plate is shown in Figs. 8-11. In the first step shown in Fig. 8, a flat transparent plate 30 is coated on one face with a flat transparent coating 31 which can be hardened with high energy radiation. Transparent plate 30 may be glass, acrylic, film, etc. Depending on its refractive index, coating 31 is thick enough to introduce a half wavelength delay to the incoming radiation.

In a second step shown in Fig. 9, a photo mask 32 of a Fresnel zone plate with alternating transparent zones 33 and dark zones 34 of the proper radii are placed on top of transparent coating 31. Dark zones 34 may be made of any suitable material which is opaque to a selected range of electromagnetic radiation. Mask 32 is the negative or reverse of a conventional Fresnel zone plate. The arrangement of transparent and dark zones shown in Fig. 9 is for making a plate with a thin center zone. Alternatively, the transparent and dark zones may be reversed for producing a thick center zone.

Transparent coating 31 is exposed to ultraviolet light or high energy radiation H, and photo mask 32 is removed. As shown in Fig. 10, the parts of transparent coating 31 which were exposed to the radiation through the transparent zones in the mask are fixated into thick transparent zones 22. The parts of transparent coating 31 which were shaded by the dark zones in the mask remain unchanged.

As shown in Fig. 11, the unchanged portions of the transparent coating are removed, preferably by etching, to produce thin transparent zones 21. Although thick transparent zones 22 and thin transparent zones 21 are not integral with each other, they are practical and very economical to make, and perform just as well as the integral zones shown in Fig. 1. The present Fresnel zone plate is much less expensive to make than curved lenses.

Fig. 12:

A third embodiment of the present Fresnel zone plate is shown in Fig. 12. It is comprised of a plate 40 with linear thin transparent zones 41 alternating with linear thick transparent zones 42. The perpendicular distances between the boundaries of the zones and the center of the central zone may be equal to those of the first or second embodiments described above.

SUMMARY AND SCOPE

Accordingly, a Fresnel zone plate is provided. It focuses radiation based on the principles of Fresnel diffraction. All of its zones are transparent constructive zones for passing all incoming radiation. It produces twice the amplitude or four times the intensity of a conventional Fresnel zone plate. It is also inexpensive to make.

Although the above description is specific, it should not be considered as a limitation on the scope of the invention, but only as an example of the preferred embodiment. Many variations are possible within the teachings of the invention. For example, the thick and thin zones may be reversed, so that the central zone may be a thick zone. Any suitable thin film coating may be used. The thin film coating may be removed with other methods. The thick zones may be made with other methods, such as iron deposit, silk screening, etc. Oval or elliptical zones may still be considered as generally circular zones. The zones may be of any other shape instead of round or linear. Therefore, the scope of the invention should be determined by the appended claims and their legal equivalents, not by the examples given.

Claims

CLAIMSI claim:

1. A Fresnel zone plate, comprising: a plate having a transparent central zone, and alternating thick transparent zones and thin transparent zones extending outwardly from said central zone, said thick transparent zones being generally identical in thickness and having generally parallel opposite faces, and said thin transparent zones being generally identical in thickness and having generally parallel opposite faces, said thick transparent zones being thicker than said thin transparent zones by a predetermined amount for generally delaying incoming destructive electromagnetic waves by an integer of at least zero plus half a wavelength, so that all electromagnetic waves are generally in phase with each other at a focal point after passing through said thick transparent zones and said thin transparent zones for increasing light intensity.

2. The Fresnel zone plate of claim 1, wherein said central zone is one of said thin transparent zones, and a next zone is one of said thick transparent zones.

3. The Fresnel zone plate of claim 1, wherein said central zone is one of said thick transparent zones, and a next zone is one of said thin transparent zones.

4. The Fresnel zone plate of claim 1, wherein an edge of said central zone has a predetermined first perpendicular distance s, to a center of said central zone generally equal to where b is a focal length of said Fresnel zone plate and λ is a wavelength of said electromagnetic waves, and boundaries between said thick transparent zones and said thin transparent zones having corresponding perpendicular distances s_n to said center of said central zone generally equal to

S_n = s, n

where n is consecutive positive integers.

5. The Fresnel zone plate of claim 1, wherein an edge of said central zone has a predetermined first perpendicular distance s, to a center of said central zone generally equal to

where b is a focal length of said Fresnel zone plate and λ is a wavelength of said electromagnetic waves, and boundaries between said thick transparent zones and said thin transparent zones having corresponding perpendicular distances s_n to said center of said central zone generally equal to

where n is consecutive positive integers, and m is consecutive positive odd integers.

6. A Fresnel zone plate, comprising: a plate having a generally circular transparent central zone, and alternating annular thick transparent zones and annular thin transparent zones extending concentrically outwardly from said central zone, said thick transparent zones being generally identical in thickness and having generally parallel opposite faces, and said thin transparent zones being generally identical in thickness and having generally parallel opposite faces, said thick transparent zones being thicker than said thin transparent zones by a predetermined amount for generally delaying incoming destructive electromagnetic waves by an integer of at least zero plus half a wavelength, so that all electromagnetic waves are generally in phase with each other at a focal point after passing through said thick transparent zones and said thin transparent zones for increasing light intensity.

7. The Fresnel zone plate of claim 6, wherein said central zone is one of said thin transparent zones, and a next zone is one of said thick transparent zones.

8. The Fresnel zone plate of claim 6, wherein said central zone is one of said thick transparent zones, and a next zone is one of said thin transparent zones.

9. The Fresnel zone plate of claim 6, wherein said central zone has a radius S] generally equal to

s, = vbλ

where b is a focal length of said Fresnel zone plate and λ is a wavelength of said electromagnetic waves, and boundaries between said thick transparent zones and said thin transparent zones have radii s_n generally equal to

where n is consecutive positive integers.

10. The Fresnel zone plate of claim 6, wherein said central zone has a radius s_t generally equal to

s_n = s, vm

10. A Fresnel zone plate, comprising: a plate having a generally linear transparent central zone, and alternating generally linear thick transparent zones and generally linear thin transparent zones extending outwardly from opposite sides of said central zone, said thick transparent zones being generally identical in thickness and having generally parallel opposite faces, and said thin transparent zones being generally identical in thickness and having generally parallel opposite faces, said thick transparent zones being thicker than said thin transparent zones by a predetermined amount for generally delaying incoming destructive electromagnetic waves by an integer of at least zero plus half a wavelength, so that all electromagnetic waves are generally in phase with each other at a focal point after passing through said thick transparent zones and said thin transparent zones for increasing light intensity.

11. The Fresnel zone plate of claim 10, wherein said central zone is one of said thin transparent zones, and a next zone is one of said thick transparent zones.

12. The Fresnel zone plate of claim 10, wherein said central zone is one of said thick transparent zones, and a next zone is one of said thin transparent zones.

13. The Fresnel zone plate of claim 10, wherein each of said opposite sides of said central zone has a predetermined first perpendicular distance s, to a center of said central zone generally equal to

s_n = s, Vn

where n is consecutive positive integers.

14. The Fresnel zone plate of claim 10, wherein each of said opposite sides of said central zone has a predetermined first perpendicular distance s, to a center of said central zone generally equal to

s_n = s, Vm

15. A method for making a Fresnel zone plate, comprising: coating a flat transparent plate with a radiation sensitive, flat transparent coating thick enough for generally delaying incoming electromagnetic waves by an integer of at least zero plus half a wavelength; positioning a photo mask on top of said fransparent coating, said photo mask having a central zone, and alternating transparent zones and opaque zones extending outwardly from said central zone; fixating said transparent coating under said transparent zones in said photo mask by exposing said transparent coating to a predetermined type of radiation; removing said photo mask; and removing unchanged portions of said transparent coating previously under said opaque zones; thereby alternating thick transparent zones and thin transparent zones are produced on said transparent plate.