CN109855558A - Digital hologram three-dimensional method for reconstructing - Google Patents

Abstract

The present invention provides a digital holographic three-dimensional reconstruction method, which comprises the following steps: S0: performing two-dimensional Fourier transform on an interference fringe image; performing two-dimensional inverse Fourier transform after analyzing and processing the Fourier frequency domain; S1: judging phase diffraction Whether the distance from the plane to the interference fringe image plane is 0, if so, execute S3; if not, execute S2; S2: Perform Fresnel digital diffraction calculation on the extracted positive interference phase information, and extract the positive optical phase of the object information, and adjust the Fresnel digital diffraction distance as the focus position to obtain the phase of the focus position; S3: Substitute the extracted positive information into the interferometry formula for calculation, and obtain the stereo height information of the object for digital holographic three-dimensional reconstruction . The method realizes high-speed, real-time, precise and stable single-exposure digital holographic measurement by analyzing an interference fringe image in the frequency domain.

Description

Three-dimensional reconstruction method of digital holography

technical field

The invention belongs to the field of digital holography, in particular to a three-dimensional reconstruction method of digital holography using two-dimensional Fourier interference fringe analysis.

Background technique

Digital holography refers to a method of digital light field reconstruction using the principle of optical interference and diffraction. Digital holography regards each point in the three-dimensional space on the surface of an opaque object that reflects light or the internal structure of transparent and translucent objects that transmit light as a point. The point light source, through the mathematical formula of digital optical interference and diffraction, uses the computer to calculate the light wave phase of these point light sources when they emit light, and realizes the ultra-precise three-dimensional measurement of the surface of opaque objects or the shape of transparent and translucent objects according to the interferometry method.

When performing ultra-precise 3D measurement of digital holography, two steps are required: the recording of interference fringes and the reconstruction of object light. The recording of interference fringes needs to be completed by building an interference optical system and using a digital camera to photograph the interference fringes; the optical reconstruction of the object needs to use digital Fresnel transform to digitally diffract the interference fringe image to obtain the phase distribution of the light in the light field of the object. Finally, the three-dimensional reconstruction is achieved using interferometry.

In the prior art, the mathematical formula of the Fresnel transform used by it is as follows:

In the above formula (1), Γ(ξ', η') is the optical complex information on the Fresnel diffraction plane, including light intensity and phase, and (ξ', η') represents the plane coordinates on the Fresnel diffraction plane , A(x, y) is the complex number information of light when the light source passes through the aperture in the aperture plane, it only contains the light intensity value, that is, the gray value of the interference fringe image, (x, y) represents the plane coordinates on the aperture plane, d represents the vertical distance between the Fresnel diffraction plane and the aperture plane, ρ′ represents the diffraction distance from a point on the aperture to a point on the Fresnel diffraction plane, λ represents the light wavelength value of the light source, and i represents a complex number.

It can be seen from the above that double integral does not have the advantage of speed in computer calculation, and has the disadvantage of cumbersome computer programming. In addition, when using formula (1) for digital holographic three-dimensional reconstruction, the interference fringes captured by the digital camera are usually directly substituted into the formula. Since the digital camera captures only the light intensity of the interference fringes, and the interference fringes are in the form of sine waves, Therefore, in the usual three-dimensional reconstruction, as shown in the following formula (2), the positive phase, negative phase and DC component of the sine wave will be reconstructed at the same time, and only the positive phase accurately reflects the shape information of the actual object, Negative phase and DC components affect accurate measurements as noise.

Among them, A(x, y) represents the gray value of the interference fringe image, and (x, y) represents the image coordinates. _AR (x, y) represents the complex variable function of the reference light, A _o (x, y) represents the complex variable function of the object light, represents the conjugate of the reference light complex function, that is, the phase is opposite, Represents the conjugate of the complex optical function of the object. B(x, y) represents the DC information in the interference fringes, Represents the negative phase information of the object light in the interference fringes, and A _o (x, y) represents the positive phase information of the object light that is really needed for 3D reconstruction.

In the above-mentioned prior art, although phase-shift digital holography can be used to extract positive object optical phase information from an image, 2-4 phase-shift interference fringe images are required, and it takes time to capture multiple phase-shift interference fringe images. In addition, the phase shift accuracy of interference fringes during the shooting process is easily affected by environmental factors such as vibration and air convection, which not only cannot achieve fast and real-time digital holographic 3D measurement, but also has strict measurement environment requirements. These factors make digital holographic measurement equipment expensive. Occasion limited.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a digital holographic three-dimensional reconstruction method. The digital holographic three-dimensional reconstruction method can quickly and real-timely extract the three-dimensional measurement data from an interference fringe image by performing frequency domain analysis on an interference fringe image. The required positive optical phase information of the object can be achieved to achieve high-speed real-time, precise and stable single-exposure digital holographic measurement.

In order to achieve the above object, the technical scheme adopted in the present invention is:

A digital holographic three-dimensional reconstruction method, comprising the following steps:

S0: Perform a two-dimensional Fourier transform on an interference fringe image to convert the interference fringe image into the Fourier frequency domain; perform two-dimensional inverse Fourier transform after analyzing and processing the Fourier frequency domain to form the image domain; and extract the positive interference phase information;

S1: Determine whether the distance from the phase diffraction plane to the interference fringe image plane is 0, if so, execute S3; if not, execute S2;

S2: perform Fresnel digital diffraction calculation on the extracted positive interference phase information, extract the positive optical phase information of the object, and adjust the Fresnel digital diffraction distance as the focus position to obtain the phase at the focus position;

S3: Substitute the extracted positive information into the interferometry formula for calculation, and obtain the stereoscopic height information of the object, so as to carry out digital holographic three-dimensional reconstruction.

As a further optimization of the present invention, in step S0, it specifically includes the following steps: first, perform a two-dimensional Fourier transform on the interference fringe image, and in the transformed Fourier frequency domain space, the positive interference phase and negative interference phase components are symmetrical to The DC component distribution in the center of the frequency domain space; then, the frequency domain information of the positive interference phase is extracted through the frequency domain space bandpass filter, and the frequency domain information of the positive interference phase is frequency shifted to the center of the frequency domain space; finally, The positive interference phase information shifted to the center of the frequency domain space is subjected to inverse Fourier transform to extract the positive interference phase information.

As a further optimization of the present invention, in step S1, it specifically includes the following steps: first, set the double Fresnel diffraction plane, that is, set the positive phase diffraction plane and the negative phase diffraction plane in the positive and negative directions symmetrically to the interference fringe image plane, respectively. Phase diffraction plane; secondly, substituting the positive interference phase into Euler's formula to obtain the complex amplitude of the interference fringes, substituting the complex amplitude of the interference fringes into the two-dimensional Fresnel digital diffraction transformation formula, and adjusting the Fresnel digital diffraction distance until the focus is obtained position, the complex amplitude of the object light at the focus position is obtained; finally, according to Euler's formula, the phase and amplitude distribution of the object light are obtained from the complex amplitude of the object light.

As a further optimization of the present invention, in step S0, the mathematical expression formula of the interference fringe image is:

C(x,y)＝2A _O (x,y)A _R (x,y)

Among them, A(x, y) is the gray value of the interference fringe image, (x, y) is the coordinate of the interference fringe image; A _R (x, y) and are the reference light complex amplitude and its conjugate, respectively; A _O (x, y) and are the complex amplitude of the object light and its conjugate, respectively; B(x, y) is the DC information in the interference fringes; is the negative interference light phase information in the interference fringes; is the positive interference light phase information in the interference fringe image; the mathematical expression formula of the two-dimensional Fourier transform of the interference fringe image is: A(f _x , f _y )=B(f _x , f _y )+C(f _x -f ₀ , f _y -f ₀ )+C ^* (f _x + _fo , f _y + _fo ),

Among them, A(f _z , f _y ) is the two-dimensional Fourier transform of the interference fringe image, (f _x , f _y ) is the center coordinate of the two-dimensional Fourier frequency domain space of the interference fringe image, and B(f _x , f _y ) is The two-dimensional Fourier transform of the DC information in the interference fringe image, C(f _z -f _o , f _y -f _o ) is the two-dimensional Fourier transform of the phase information of the positive interference light in the interference fringe, C ^* (f _x +f ₀ , f _y +f ₀ ) is the two-dimensional Fourier transform of the negative interference light phase information in the interference fringes, f _o is the two-dimensional Fourier-transformed frequency domain coordinates of the positive or negative interference light phase information and the two-dimensional Fourier frequency domain intermediate center coordinates deviation.

As a further optimization of the present invention, in step S2, the two-dimensional Fresnel digital diffraction transformation formula is: Among them, Γ(ξ, η) is the complex amplitude of the object light on the positive phase diffraction plane, E ₀ (x, y) represents the complex amplitude of interference fringes;

As a further optimization of the present invention, in step S1, the two-dimensional Fresnel digital diffraction transformation formula is: Among them, Γ(ξ', η') is the complex amplitude of the object light on the negative phase diffraction plane, Among them, B ₀ (x, y) represents the complex amplitude of interference fringes;

As a further optimization of the present invention, in step S1, the Euler formula is: in, is the phase, and i is a complex number.

As a further optimization of the present invention, in step S0, the Fresnel transformation formula on which the Fresnel digital diffraction is based is: Among them, Γ(ξ', η') is the optical complex number information on the Fresnel diffraction plane, which are the light intensity and phase respectively; (ξ', η') are the plane coordinates on the Fresnel diffraction plane; A(x , y) is the complex number information of light when the light source passes through the aperture in the aperture plane; (x, y) is the plane coordinate on the aperture plane; d is the vertical distance between the Fresnel diffraction plane and the aperture plane; ρ' is the aperture Diffraction distance from a point on the Fresnel diffraction plane to a point on the Fresnel diffraction plane; λ is the light wavelength value of the light source, and i is a complex number.

Compared with the prior art, the advantages and positive effects of the present invention are as follows: the digital holographic three-dimensional reconstruction method of the present invention can extract three-dimensional measurements from an interference fringe image quickly and in real time by performing frequency domain analysis on an interference fringe image. The required positive optical phase information of the object can achieve high-speed real-time and precise and stable single-exposure digital holographic measurement.

Description of drawings

Fig. 1 is the flow chart of the digital holographic three-dimensional reconstruction method of the present invention;

Fig. 2 is the frequency domain distribution diagram after interference fringe image and its two-dimensional Fourier transform in the method of the present invention;

3 is a plan view of Gemini set Fresnel diffraction in the method of the present invention;

4 is a schematic diagram of moving bandpass filtered frequency domain information to the center of the entire frequency domain in the method of the present invention;

Fig. 5 is the phase distribution diagram after two-dimensional Fourier transform in the method of the present invention;

6 is an amplitude distribution diagram after two-dimensional Fourier transform in the method of the present invention;

7 is a schematic diagram of adjusting the diffraction distance to obtain focused diffraction imaging in the method of the present invention;

FIG. 8 is a schematic diagram of the result of digital holographic three-dimensional reconstruction in the method of the present invention.

Detailed ways

Hereinafter, the present invention will be specifically described through exemplary embodiments. It should be understood, however, that elements, structures and features of one embodiment may be beneficially combined in other embodiments without further recitation.

As shown in FIG. 1, the present invention provides a digital holographic three-dimensional reconstruction method, and the digital holographic three-dimensional reconstruction method includes the following steps:

S0: Perform a two-dimensional Fourier transform on an interference fringe image to convert the interference fringe image into the Fourier frequency domain; perform two-dimensional inverse Fourier transform after analyzing and processing the Fourier frequency domain to form the image domain; and extract the positive interference phase information;

S1: Determine whether the distance from the phase diffraction plane to the interference fringe image plane is 0, if so, execute S3; if not, execute S2;

S2: Perform the Fresnel digital diffraction calculation on the extracted positive interference phase information, extract the positive optical phase information of the object, and adjust the Fresnel digital diffraction distance as the focus position to obtain the phase at the focus position; as shown in Figure 7 The bottom image in the figure is the phase information of the focus position;

S3: Substitute the extracted positive information into the interferometry formula for calculation, and obtain the stereoscopic height information of the object, so as to carry out digital holographic three-dimensional reconstruction.

Further, in step S0, it specifically includes the following steps: first, perform a two-dimensional Fourier transform on the interference fringe image, and in the transformed Fourier frequency domain space, the positive interference phase and negative interference phase components are symmetrical to the center of the frequency domain space. Then, the frequency domain information of the positive interference phase is extracted by the frequency domain space bandpass filter, and the frequency domain information of the positive interference phase is frequency shifted to the center of the frequency domain space; finally, the frequency domain information is shifted to the frequency domain. The positive interference phase information in the center of the space is subjected to inverse Fourier transform to extract the positive interference phase information.

As shown in Figure 3, in the Fourier frequency domain space after the two-dimensional Fourier transform, the frequency domain value in the center is the DC component of the interference fringes, the value range in the lower left corner is the positive object light phase component in the interference fringes, and the value in the upper right corner is the positive light phase component of the object in the interference fringes. The value range is the negative object light phase component in the interference fringes. The positive phase component in the lower left corner can be extracted by the two-dimensional frequency domain bandpass filter, and the DC component and the negative phase component can be directly filtered out. Specifically, as shown in Figure 4, the frequency domain information after bandpass filtering needs to pass two-dimensional inverse Fourier transform to obtain the complex optical function of the object in the time domain, but the frequency domain information after bandpass filtering has lost DC and negative. Phase information requires moving the bandpass filtered frequency domain components to the center of the frequency domain to compensate for the missing DC and negative phase components.

Continuing as shown in Figure 5 and Figure 6, the two-dimensional inverse Fourier transform of the frequency domain shown on the right in Figure 4 can be used to obtain the complex function of the interference fringes, that is, A(x, y) in Equation 1, according to Euler's formula can get the phase and amplitude distribution.

In addition, in the above, in step S0, the mathematical expression formula of the interference fringe image is:

C(x,y)＝2A _O (x,y)A _R (x,y)

Among them, A(x, y) is the gray value of the interference fringe image, (x, y) is the coordinate of the interference fringe image; A _R (x, y) and are the reference light complex amplitude and its conjugate, respectively; A _O (x, y) and are the complex amplitude of the object light and its conjugate, respectively; B(x, y) is the DC information in the interference fringes; is the negative interference light phase information in the interference fringes; is the positive interference light phase information in the interference fringe image; the mathematical expression formula of the two-dimensional Fourier transform of the interference fringe image is: A(f _x , f _y )=B(f _x , f _y )+C(f _x -f ₀ , f _y -f ₀ )+C ^* (f _x +f ₀ , f _y +f ₀ ),

Among them, A(f _x , f _y ) is the two-dimensional Fourier transform of the interference fringe image, (f _x , f _y ) is the center coordinate of the two-dimensional Fourier frequency domain space of the interference fringe image, and B(f _x , f _y ) is The two-dimensional Fourier transform of the DC information in the interference fringe image, C(f _x -f _o , f _y -f _o ) is the two-dimensional Fourier transform of the phase information of the positive interference light in the interference fringe, C ^* (f _x +f ₀ , f _y +f ₀ ) is the two-dimensional Fourier transform of the negative interference light phase information in the interference fringes, f ₀ is the two-dimensional Fourier-transformed frequency domain coordinates of the positive or negative interference light phase information and the two-dimensional Fourier frequency domain intermediate center coordinates deviation.

In step S0, the Fresnel transformation formula on which the Fresnel digital diffraction is based is: Among them, Γ(ξ', η') is the optical complex number information on the Fresnel diffraction plane, which are the light intensity and phase respectively; (ξ', η') are the plane coordinates on the Fresnel diffraction plane; A(x , y) is the complex number information of light when the light source passes through the aperture in the aperture plane; (x, y) is the plane coordinate on the aperture plane; d is the vertical distance between the Fresnel diffraction plane and the aperture plane; A is the aperture on the aperture Diffraction distance when a point is diffracted to a point on the Fresnel diffraction plane; λ is the light wavelength value of the light source, and i is a complex number.

Continue as shown in FIG. 2 , in step S1 , the following steps are specifically included: First, set the double Fresnel diffraction plane, that is, set the positive phase diffraction plane 2 in the positive and negative directions symmetrical to the interference fringe image plane 1 respectively and the negative phase diffraction plane 3, the distance between the positive phase diffraction plane 2 and the interference fringe image plane 1 is the positive diffraction distance 4, and the distance between the negative phase diffraction plane 3 and the interference fringe image plane 1 is the negative Second, the positive interference phase is substituted into Euler's formula to obtain the complex amplitude of the interference fringes, and the complex amplitude of the interference fringes is substituted into the two-dimensional Fresnel digital diffraction transformation formula, and the Fresnel digital diffraction distance is adjusted until obtaining Focusing position, the object light complex amplitude at the focus position is obtained; finally, according to Euler's formula, the object light phase and amplitude distribution are obtained from the object light complex amplitude.

In the above, in step S1, the two-dimensional Fresnel digital diffraction transformation formula is Among them, Γ(ξ', η') is the complex amplitude of the object light on the negative phase diffraction plane, Among them, E ₀ (x, y) represents the complex amplitude of interference fringes; Meanwhile, in the above step S1, the Euler formula is: in, is the phase, and i is a complex number.

In step S2, the two-dimensional Fresnel digital diffraction transformation formula is Among them, Γ(ξ, η) is the complex amplitude of the object light on the positive phase diffraction plane, E ₀ (x, y) represents the complex amplitude of interference fringes;

Through the above-mentioned digital holographic three-dimensional reconstruction method, the reconstruction result is shown in Figure 8. The present invention analyzes an interference fringe image in the frequency domain by means of a two-dimensional Fourier transform, and extracts three-dimensional images from an interference fringe image in a fast and real-time manner. The required positive optical phase information of the object is measured, thereby realizing high-speed real-time, precise and stable single-exposure digital holographic measurement. At the same time, the digital holographic three-dimensional reconstruction method of the present invention does not need to shoot multiple phase-shifted interference fringe images as in the prior art, which reduces the time spent on shooting, and is not affected by environmental factors such as vibration and air convection, thereby achieving rapid Real-time digital holographic 3D measurement has wider applications and lower costs.

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention. should be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (8)

1. a digital holographic three-dimensional reconstruction method, is characterized in that: comprise the following steps: S0: Perform a two-dimensional Fourier transform on an interference fringe image to convert the interference fringe image into the Fourier frequency domain; perform two-dimensional inverse Fourier transform after analyzing and processing the Fourier frequency domain to form the image domain; and extract the positive interference phase information; S1: Determine whether the distance from the phase diffraction plane to the interference fringe image plane is 0, if so, execute S3; if not, execute S2; S2: perform Fresnel digital diffraction calculation on the extracted positive interference phase information, extract the positive optical phase information of the object, and adjust the Fresnel digital diffraction distance as the focus position to obtain the phase at the focus position; S3: Substitute the extracted positive information into the interferometry formula for calculation, and obtain the stereoscopic height information of the object, so as to carry out digital holographic three-dimensional reconstruction. 2. digital holographic three-dimensional reconstruction method according to claim 1, is characterized in that: in step S0, specifically comprises the following steps: first, two-dimensional Fourier transform is carried out to the interference fringe image, and in the transformed Fourier frequency domain space, the positive The interference phase and the negative interference phase components are symmetrical to the DC components located in the center of the frequency domain space; then the frequency domain information of the positive interference phase is extracted through the frequency domain space bandpass filter, and the frequency domain information of the positive interference phase is extracted. The information frequency is shifted to the center of the frequency domain space; finally, the positive interference phase information shifted to the center of the frequency domain space is subjected to inverse Fourier transform to extract the positive interference phase information. 3. The three-dimensional reconstruction method of digital holography according to claim 1 or 2, characterized in that: in step S1, the method specifically comprises the following steps: firstly, setting the double Fresnel diffraction plane, that is, symmetrical to the interference fringe image plane at The positive phase diffraction plane and the negative phase diffraction plane are respectively set in the positive and negative directions; secondly, the positive interference phase is substituted into Euler's formula to obtain the complex amplitude of the interference fringes, and the complex amplitude of the interference fringes is substituted into the two-dimensional Fresnel digital diffraction Modify the formula and adjust the Fresnel digital diffraction distance until the focus position is obtained, and the complex amplitude of the object light at the focus position is obtained; finally, according to Euler's formula, the phase and amplitude distribution of the object light are obtained from the complex amplitude of the object light. 4. The digital holographic three-dimensional reconstruction method according to claim 2, wherein in step S0, the mathematical expression formula of the interference fringe image is: Among them, A(x, y) is the gray value of the interference fringe image, (x, y) is the coordinate of the interference fringe image; A _R (x, y) and are the reference light complex amplitude and its conjugate, respectively; A _O (x, y) and are the complex amplitude of the object light and its conjugate, respectively; B(x, y) is the DC information in the interference fringes; is the negative interference light phase information in the interference fringes; is the positive interference light phase information in the interference fringe image; the mathematical expression formula of the two-dimensional Fourier transform of the interference fringe image is: A(f _x , f _y )=B(f _x , f _y )+C(f _x -fo , f _y -f _{o )} +C ^* (f _x + _fo , f _y +f ₀ ), Among them, A(f _x , f _y ) is the two-dimensional Fourier transform of the interference fringe image, (f _x , f _y ) is the center coordinate of the two-dimensional Fourier frequency domain space of the interference fringe image, and B(f _x , f _y ) is The two-dimensional Fourier transform of the DC information in the interference fringe image, C(f _x · f ₀ , f _y · f ₀ ) is the two-dimensional Fourier transform of the positive interference light phase information in the interference fringe, C ^* (f _x +f ₀ , f _y +f ₀ ) is the two-dimensional Fourier transform of the negative interference light phase information in the interference fringes, and f _o is the frequency domain coordinate after the two-dimensional Fourier transform of the positive or negative interference light phase information Deviation from the mid-center coordinate in the 2D Fourier frequency domain. 5. The digital holographic three-dimensional reconstruction method according to claim 3, wherein in step S2, the two-dimensional Fresnel digital diffraction transformation formula is: Among them, Γ(ξ, η) is the complex amplitude of the object light on the positive phase diffraction plane, E ₀ (x, y) represents the complex amplitude of interference fringes; 6. The digital holographic three-dimensional reconstruction method according to claim 3, wherein in step S1, the two-dimensional Fresnel digital diffraction transformation formula is: Among them, Γ(ξ', η') is the complex amplitude of the object light on the negative phase diffraction plane, Among them, E ₀ (x, y) represents the complex amplitude of interference fringes; 7. The digital holographic three-dimensional reconstruction method according to claim 3, wherein in step S1, the Euler formula is: in, is the phase, and i is a complex number. 8. The digital holographic three-dimensional reconstruction method according to claim 1, wherein in step S0, the Fresnel transform formula on which the Fresnel digital diffraction is based is: Among them, Γ(ξ', η') is the optical complex number information on the Fresnel diffraction plane, which are the light intensity and phase respectively; (ξ', η') are the plane coordinates on the Fresnel diffraction plane; A(x , y) is the complex number information of light when the light source passes through the aperture in the aperture plane; (x, y) is the plane coordinate on the aperture plane; d is the vertical distance between the Fresnel diffraction plane and the aperture plane; ρ′ is the aperture Diffraction distance from a point on the Fresnel diffraction plane to a point on the Fresnel diffraction plane; λ is the light wavelength value of the light source, and i is a complex number.