CN116560202A - A scanning holographic device for obtaining only horizontal parallax holograms - Google Patents

Abstract

The invention discloses a scanning holographic device for obtaining only horizontal parallax holograms, including: a focusing lens, a light source, a pupil, a plane mirror, an acousto-optic modulator (AOM), a two-dimensional scanning vibrating mirror, a cylindrical mirror, a horizontal narrow slit; the present invention uses the cylindrical lens to compensate the vertical axis data, and then uses the confinement of the horizontal slit to process the two-dimensional Fresnel zone plate, and converts the two-dimensional Fresnel wave representation into a one-dimensional Fresnel wave that reduces the curvature of the vertical axis. Neil zone plate, and then use a one-dimensional Fresnel zone plate to scan the object, the photoelectric sensor records the light wave, and then uses the computer to synthesize the recorded data to obtain the only horizontal parallax hologram of the object; the advantage of the present invention is : Low cost, easy to build and operate the optical path, effectively increase the calculation speed of the hologram, using the scanning holographic optical path as the base, can increase the anti-interference performance of the experimental platform optical path; use one-dimensional Fresnel zone plate for scanning, can be simplified Horizontal parallax-only scanning holograms with better reproduction while reducing the amount of data.

Description

A scanning holographic device for obtaining only horizontal parallax holograms

technical field

The invention relates to a scanning holographic device for obtaining only horizontal parallax holograms, belonging to the technical field of holographic optics.

Background technique

Holography (Optical Holography) is an imaging technique consisting of recording and reconstruction. The shooting process uses the principle of interference to record the light wave information of the object, that is, the object to be photographed forms a diffuse object beam under laser irradiation; another part of the laser light is used as a reference beam to irradiate the holographic film, and interferes with the object beam superposition, and the object light wave The phase and amplitude of each point on the surface are converted into spatially varying intensities, so that all information of the light wave of the object can be recorded by using the contrast and interval between the interference fringes; Become a hologram, or hologram; then use the principle of diffraction to reproduce the light wave information of the object, which is the imaging process: the hologram is like a complex optical holographic grating, under the irradiation of coherent laser, a linearly recorded sinusoidal hologram Generally, two images can be given by the diffracted light wave, that is, the original image (also known as the initial image) and the conjugate image. The reproduced image has a strong three-dimensional effect and has a real visual effect. Each part of the hologram records the optical information of each point on the object, so in principle, each part of it can reproduce the entire image of the original object, and multiple different images can be recorded on the same film through multiple exposures. are displayed separately.

To obtain a high-quality and large-size hologram, the registration and reconstruction of high-quality and large-size holograms has always been a heavy computational task for computers. A high-quality or large-size hologram requires billions or more pixels, which brings a large amount of space-bandwidth product. The extensive use of space-bandwidth products has seriously affected the storage and manipulation of holograms. In order to reduce the burden on the computer and obtain large-size or high-quality holograms, according to the characteristics that the human eye is sensitive to the parallax of the horizontal axis but not sensitive to the parallax of the vertical axis, the present invention proposes a hologram with only horizontal parallax. Parallax holograms have a large viewing angle in the x direction to maintain high quality while maintaining a low spatial bandwidth product.

It can be seen that how to obtain a hologram with only horizontal parallax is the key to obtaining a high-quality hologram with only horizontal parallax in the present invention.

Contents of the invention

The present invention aims at the constraints of the prior art. The purpose of the present invention is to provide a scanning holographic device implementation method for obtaining only horizontal parallax holograms, which makes up for the deficiencies in the prior art.

In order to realize above object of the invention, the technical scheme that the present invention takes is as follows:

A scanning holographic device for obtaining only horizontal parallax holograms, characterized in that it includes a laser 1, a beam splitter 2, an acousto-optic modulator 3, a plane mirror 4, a pupil I5 (denoted as p ₁ (x, y)), Pupil Ⅱ17 (denoted as p ₂ (x, y)), Fourier lens Ⅰ6, Fourier lens Ⅱ18, Fourier lens Ⅲ19, beam combiner 7, cylindrical mirror 8, horizontal slit 9, two-dimensional Scanning mirror 10, scanned object Γ(x, y)11, photoelectric sensor PD12, band-pass filter BPF13, electronic multiplier cosΩt14, electronic multiplier sinΩt20, low-pass filter 15, computer 16,

Laser 1 emits a beam of laser light with a frequency ω, and after passing through the beam splitter 2, it becomes two beams of light with the same frequency; a beam of light (denoted as the upper light) passes through the acousto-optic modulator 3 to change the frequency to (ω+Ω), and then After passing through the plane mirror 4, pupil II17, and Fourier lens III19, it reaches the beam combining mirror 7; the frequency of the other beam of light (denoted as the lower light) remains unchanged, and it passes through the pupil I5 and the Fourier lens II18 to arrive at the beam combining mirror. Beam mirror 7; two beams of light with different frequencies are modulated through pupil I5 and pupil II17, and interference is generated at the position of beam combiner mirror 7, and the interference pattern is a Fresnel zone ring; the interference light passes through cylindrical mirror 8 and rectangular The horizontal slit 9 is processed to obtain an approximately one-dimensional curvature-free narrow-band Fresnel zone plate, and then the two-dimensional scanning galvanometer 10 is used to allow the interference light to scan the target object Γ(x, y)11; The light propagates to the photoelectric sensor PD12 through the Fourier lens Ⅰ6, and generates an electrical signal i(x,y) related to the amplitude information of the object; the electrical signal i(x,y) passes through the band-pass filter BPF13, the electronic multiplier cosΩt14, The electronic multiplier sinΩt20 and the low-pass filter 15 enter the computer 16, and the computer 16 performs image recording, reproduction and post-processing on the electrical signal i(x, y).

Preferably, the pupil function of the pupil I5 in the present invention is set to p ₁ (x,y)=δ(x,y), and the pupil function of the pupil II17 is set to p ₂ (x,y)=1.

Preferably, the position of the pupil I5 in the present invention is located on the front focal plane of the Fourier lens II18, and the position of the pupil II17 is located on the front focal plane of the Fourier lens III19.

Preferably, the position of the two-dimensional scanning galvanometer 10 in the present invention is located at the back focal plane of the Fourier lens I6 and the Fourier lens II18.

Preferably, the splitting ratio of the beam splitter 2 in the present invention is 1:1.

Principle of the present invention:

Assume that the initial phases of the two light fields after the laser passes through the beam splitter 2 are the same, define the propagation direction of the light as z, and the propagation distance of the light as the value of z, define the x and y coordinates respectively according to the method of the Cartesian coordinate system, and define The propagation time elapsed from the laser source is t, and the expressions are:

In the formula, represents the complex light field of the upper light, /> Represents the complex light field of the lower light, A represents the amplitude of the upper light, B represents the amplitude of the lower light, j is the imaginary number unit, ω represents the frequency of the laser, Ω represents the heterodyne frequency of the acousto-optic modulator,

The upper light passes through the acousto-optic modulator 3, and the frequency becomes ω+Ω; the frequency of the lower light remains unchanged at ω. If the two lights directly interfere at this time, the resulting interference light field can be expressed as:

Then use the PD to receive the optical signal, and the electrical signal i generated by the photoelectric sensor is only related to the amplitude of the optical signal, that is:

The formula contains amplitude and phase related information, which is the advantage of the optical heterodyne method.

It is now known that the transparent object t(x, y) located at d in front of the convex lens with focal length f is shown in Figure 2 under plane wave illumination. It can be seen from the figure that the plane light illuminates the transparent object t(x, y) Then it passes through a convex lens and forms an image on the back focal plane.

The calculation block diagram is shown in Figure 3. It can be seen from the figure that the transparent object t(x, y) reaches the lens after diffraction, and then continues to diffract to the back focal plane after phase modulation of the lens.

in Then it can be concluded that:

ψ _p (x,y; f)={[t(x,y)*h(x,y;d)]t _f (x,y)}*h(x,y;f) (5)

Where "*" represents the convolution operation, ψ _p (x, y; f) represents the complex optical field information of the back focal plane of the lens, t _f (x, y) represents the phase factor of the lens, h(x, y; d) Represents the Fresnel diffraction point spread function with a distance of d, h(x,y; f) represents the Fresnel diffraction point spread function with a distance of f, and k represents the wave number of light. After ignoring some constants, the above formula can be written for:

In the optical path of the present invention, the situation of getting d=f, by ignoring some constants, the above formula becomes:

k _y = k _y /f

where k _x , _ky represent the coordinates in the frequency domain, Indicates the complex optical field information of t(x, y) after passing through the system in Figure 2. Similarly, P ₁ P ₂ in the following formula represents the complex optical field information of p ₁ p ₂ after passing through the system in Figure 2; by formula (7) After the two light beams respectively pass through the pupil p ₁ (x,y) and p ₂ (x,y) and the lenses L1 and L2, the light field /> respectively expressed as

After the two beams interfere at BS ₂ , the resultant interference light field expression Can be expressed as:

Here, the form of a two-dimensional Fresnel zone plate is formed, and the Fresnel zone plate is processed to convert it into an approximately one-dimensional narrow-band Fresnel zone plate, as shown in Figure 3 below. It can be seen from the figure that the Schematic representation of a processed approximately 1D narrow-band Fresnel zone plate.

As shown in Figure 3, the present invention uses the approximately one-dimensional curvature-free narrow-band Fresnel zone plate to replace the two-dimensional Fresnel zone plate in the optical scanning holography (OSH) to scan the target three-dimensional object. In the simulation, The present invention uses the method of plane wave and spherical wave interference to obtain the required two-dimensional Fresnel zone plate, and then uses a large-curvature cylindrical mirror to eliminate the Y-axis curvature of the two-dimensional Fresnel zone plate to obtain Y axis data compensation, which can effectively increase the online effect of the holographic vertical axis direction, as follows:

Afterwards, use a two-dimensional window function to limit the data on the vertical axis, and obtain an approximately one-dimensional narrow-band Fresnel zone plate that retains the complete state of the X-axis and discards most of the data on the Y-axis.

Where rect represents the window function, 1/η determines the range of 1D FZP along the vertical direction, Represents the light field expression for the processed approximately one-dimensional narrow-band Fresnel zone plate.

Then the Y-axis curvature is eliminated, and after processing by the window function rect, the approximately one-dimensional narrow-band Fresnel zone plate can be expressed as:

in Represents the light field expression of the processed quasi-one-dimensional narrow-band Fresnel zone plate.

Using interference light to scan the object at the distance scanning mirror z, the current signal output by the photoelectric sensor PD is:

Where Γ represents the transmittance function of the object, x', y' represent the coordinates on the surface of the photoelectric sensor PD, the above electrical signal is filtered by a BPF with a center frequency of iΩ, and then the real part is taken, and the obtained current signal _iΩ is:

Where Re represents the real part of the complex function in parentheses, Represents the conjugate of P ₁ , the above formula reflects the relationship between the input signal and the output signal in the whole system, if i _Ω (x, y; z; t) = Re(i _Ωp (x, y; z ; t)·e ^jΩt ), where Then the optical transfer function (Optical Transfer Function, OTF) can be expressed as:

When the pupil function is set as p ₁ (x,y)=δ(x,y), p ₂ (x,y)=1, it can be obtained:

Among them, "*" represents the convolution operation. According to (12), using the relationship between convolution and Fourier transform, it can be known that the finally obtained electrical signal can be expressed as:

The current signal goes through the modulator After that, the signal is extracted by sin(Ωt) and cos(Ωt) respectively, the real part i _cos and the imaginary part i _sin :

Where Im represents the imaginary part of the complex function in brackets, H _cos and H _sin represent the cos hologram and sin hologram respectively; combining the above two formulas, the composite hologram H _HPO (x, y; z) can be obtained as:

Using (21), the approximately one-dimensional narrow-band Fresnel zone plate is interfered with the three-dimensional object to obtain a hologram containing only the horizontal parallax information of the object. Finally, the present invention reproduces the obtained hologram with reference light to obtain its reproduction effect.

Here the present invention claims (21) that the recorded hologram is only a horizontal parallax hologram; since the recorded hologram is a pattern of only horizontal parallax encoding between the intensity of the object and the approximately one-dimensional narrow-band FZP, this The invention can directly obtain only the horizontal parallax scanning hologram required by the present invention; meanwhile, this hologram is also obtained by scanning holography, therefore, the hologram can reconstruct the three-dimensional image of the target without double-image noise; in order to reduce The required amount of data, the present invention uses an approximately one-dimensional narrow-band Fresnel zone plate to scan to convert a full parallax hologram into a horizontal parallax-only (HPO) hologram, and proposes a HPO hologram for 3D display; The invention believes that this can be an excellent way to reduce the amount of data required for 3D display; the full parallax hologram of a 3D object can be considered as a collection of 2D FZPs, while the HPO hologram is a collection of 1D FZPs; accordingly, the HPO Holograms can be thought of as objects whose intensity is encoded with 1D FZP.

Regarding the reproduction process of the holographic image, for the holographic image that has been recorded, if the target object is at the position z from the scanning galvanometer, it should be reproduced at the distance z. Using the Fresnel diffraction formula, the reproduced image I(x, y; z) can be expressed as:

I(x,y;z)=H _HPO (x,y;z)*h(x,y;z) (22)

That is, the convolution of the hologram and the Fresnel transfer function in the spatial domain, where h(x,y; z) represents the Fresnel diffraction point spread function at z; at the same time, the cos hologram I _cos (x,y; z) and the sin hologram I _sin (x, y; z) can be expressed as:

I _cos (x,y;z)=H _cos (x,y;z)*h(x,y;z) (23)

I _sin (x, y; z) = H _sin (x, y; z)*h (x, y; z) (24)

Beneficial effects of the present invention:

The device of the present invention has low cost, simple construction and operation of the optical path, effectively increases the calculation speed of the hologram, uses the scanning holographic optical path as the base, and can increase the anti-interference performance of the optical path of the experimental platform; uses a one-dimensional Fresnel zone plate for scanning , it is possible to obtain a horizontal parallax-only scanning hologram with a reduced data volume and a better reproduction effect.

Description of drawings

Fig. 1 overall structural light path diagram of the present invention;

Figure 2 is a schematic diagram of plane wave irradiation;

Figure 3 is a block diagram of plane wave irradiation calculation;

Fig. 4 is a schematic diagram of an approximately one-dimensional narrow-band Fresnel zone plate.

In the figure: 1-laser; 2-beam splitter; 3-acousto-optic modulator; 4-plane mirror; 5-pupil Ⅰ; 6-Fourier lens Ⅰ; 7-beam combiner; 8-cylindrical mirror; 9-horizontal slit; 10-two-dimensional scanning galvanometer; 11-scanned object Γ(x,y); 12-photoelectric sensor PD; 13-bandpass filter BPF; 14-electronic multiplier cosΩt; 15-low Pass filter; 16-computer; 17-pupil II; 18-Fourier lens II, 19-Fourier lens III; 20-electronic multiplier sinΩt.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and examples.

Example 1

A scanning holographic device for obtaining only horizontal parallax holograms, as shown in Figure 1, includes a laser 1, a beam splitter 2, an acousto-optic modulator 3, a plane mirror 4, and a pupil I5 (denoted as p ₁ (x, y) ), pupil II17 (denoted as p ₂ (x,y)), Fourier lens I6, Fourier lens II18, Fourier lens III19, beam combiner 7, cylindrical mirror 8, horizontal slit 9, Two-dimensional scanning galvanometer 10, scanned object Γ(x, y) 11, photoelectric sensor PD12, band-pass filter BPF13, electronic multiplier cosΩt14, electronic multiplier sinΩt20, low-pass filter 15, computer 16, laser 1 emission A beam of laser light with a frequency ω passes through the beam splitter 2 and becomes two beams of the same frequency; a beam of light passes through the acousto-optic modulator 3 to change the frequency to (ω+Ω), and passes through the plane mirror 4, pupil II 17, Fu The Liye lens III19 reaches the beam combiner 7; the frequency of the other beam of light remains unchanged at ω, and then passes through the pupil I5 and the Fourier lens II18 to reach the beam combiner 7; two beams of light with different frequencies pass through the pupil I5, The pupil II17 completes the modulation, and produces interference at the position of the beam combiner 7, and the interference pattern is a Fresnel zone ring; the interference light is processed by the cylindrical mirror 8 and the rectangular horizontal slit 9 to obtain an approximately one-dimensional curvature-free narrow-band phenanthrene Neel zone plate, and then use the two-dimensional scanning galvanometer 10 to let the interference light scan the target object Γ(x, y)11; the light containing the object amplitude information propagates to the photoelectric sensor PD12 through the Fourier lens I6, and generates the same The electrical signal i(x,y) related to the amplitude information of the object; the electrical signal i(x,y) enters the computer 16 through the band-pass filter BPF13, the electronic multiplier cosΩt14, the electronic multiplier sinΩt20, and the low-pass filter 15 in sequence. 16 pairs of electrical signals i(x,y), and then i(x,y) first passes through a bandpass filter to tune the heterodyne frequency Ω, in order to filter the current baseband and extract the heterodyne current; the heterodyne current is split into two channels And obtained two output: the common integrated circuit of ic and is, the cosine or sine input signal and the heterodyne frequency by electron multiplication, then use the heterodyne current of low-pass filter extraction stage; The heterodyne current that the present invention will obtain After storage in a computer, a horizontal parallax-only hologram without double-image noise is finally obtained.

As a preferred embodiment of the present invention, the position of the pupil I5 is located on the front focal plane of the Fourier lens II18, and the position of the pupil II17 is located on the front focal plane of the Fourier lens III19.

As a preferred embodiment of the present invention, the two-dimensional scanning galvanometer 10 is located at the back focal plane of the Fourier lens I6 and the Fourier lens II18.

As a preferred embodiment of the present invention, the splitting ratio of the beam splitter 2 is 1:1.

Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that it can be described in terms of form and Various changes may be made in the details without departing from the scope of the invention defined by the claims.

Claims (6)

1. A scanning hologram device for obtaining a horizontal parallax only hologram, characterized by: comprises a laser (1), a beam splitter (2), an acousto-optic modulator (3), a plane mirror (4), a pupil I (5), a pupil II (17), a Fourier lens I (6), a Fourier lens II (18), a Fourier lens III (19), a beam combining mirror (7), a cylindrical mirror (8), a horizontal slit (9), a two-dimensional scanning galvanometer (10), a scanned object Γ (x, y) (11), a photoelectric sensor PD (12), a band-pass filter BPF (13), an electronic multiplier cos omega t (14), an electronic multiplier sin omega t (20), a low-pass filter (15) and a computer (16),

the laser (1) emits a beam of laser with the frequency omega, and the laser passes through the spectroscope (2) and then becomes two beams of light with the same frequency; a beam of light changes the frequency into (omega+omega) through the acousto-optic modulator (3), and sequentially passes through the plane mirror (4), the pupil II (17) and the Fourier lens III (19) to reach the beam combining mirror (7); the frequency of the other beam of light is still omega, and the other beam of light sequentially passes through the pupil I (5) and the Fourier lens II (18) to reach the beam combining lens (7); two beams of light with different frequencies pass through a pupil I (5) and a pupil II (17) to finish modulation, interference is generated at the position of a beam combining lens (7), and an interference pattern is a Fresnel wave band ring; the interference light is processed through a cylindrical mirror (8) and a rectangular horizontal slit (9) to obtain a curvature-free narrow-band Fresnel zone plate, and then a two-dimensional scanning galvanometer (10) is used for scanning the interference light on a target object Γ (x, y) (11); light containing the object amplitude information propagates through the fourier lens i (6) to the photosensor PD (12), generating an electrical signal i (x, y) related to the object amplitude information; the electric signal i (x, y) sequentially passes through a band-pass filter BPF (13), an electronic multiplier cos omega t (14), an electronic multiplier sin omega t (20) and a low-pass filter (15) to enter a computer (16), and the computer (16) records, reproduces and post-processes the image of the electric signal i (x, y) to finally obtain the horizontal parallax hologram without double image noise.

2. Scanning holographic device for obtaining a horizontal parallax only hologram according to claim 1, wherein: the pupil function of pupil I (5) is set to p ₁ (x, y) =δ (x, y), the pupil function of pupil ii (17) is set to p ₂ (x,y)＝1。

3. Scanning holographic device for obtaining a horizontal parallax only hologram according to claim 1, wherein: the pupil I (5) is located on the front focal plane of the Fourier lens II (18), and the pupil II (17) is located on the front focal plane of the Fourier lens III (19).

4. Scanning holographic device for obtaining a horizontal parallax only hologram according to claim 1, wherein: the two-dimensional scanning galvanometer (10) is positioned at the back focal planes of the Fourier lens I (6) and the Fourier lens II (18).

5. Scanning holographic device for obtaining a horizontal parallax only hologram according to claim 1, wherein: the beam splitting ratio of the beam splitter (2) is 1:1.

6. Scanning holographic device for obtaining a horizontal parallax only hologram according to claim 1, wherein: hologram H _HPO The expression of (x, y; z) is:

wherein: defining the propagation direction of light as z, defining x and y coordinates respectively according to Cartesian coordinate system, j as imaginary unit, k as wave number of light, rect as window function, 1/η determining the range of 1D FZP along vertical direction, H _cos And H is _sin Representing cos hologram and sin hologram, respectively, Γ (x, y; z) being a transmittance function, k, comprising information of the target object _x ，k _y Representing the coordinates in the frequency domain,is an inverse fourier transform form of the Optical Transfer Function (OTF).