TWI815382B - Method of generating holographic images - Google Patents

Abstract

The present invention provides a method for generating holographic images. The method includes the following steps. A controller generates multiple phase distributions corresponding to multiple target images. The controller superimposes the multiple phase distributions to obtain a phase-only mask. The phase-only mask is input to a spatial light modulator, so that the spatial light modulator represents the phase-only mask. An illuminating beam is generated by a light source to enter the spatial light modulator, and the spatial light modulator converts the illuminating beam into an image beam to generate a plurality of virtual images corresponding to the plurality of target images, wherein the plurality of virtual images Located in different locations in space.

Description

Methods of producing holographic images

The present invention relates to an optical imaging method, in particular to a method of generating a holographic image.

Computer-generated holography (CGH), which can produce true three-dimensional images, has been widely used in many fields, including in wearable devices or various holographic displays. Generally speaking, if you want to simultaneously reconstruct multiple target images with different depths, different positions, or different tilt angles, you need to have multiple imaging systems at the same time to generate corresponding target images, resulting in a system that is too bulky and increases system manufacturing costs. In addition, limited by the tolerances during the assembly of the imaging system, as well as the limitations of the hardware and optical components of the imaging system, general imaging systems cannot correct the generated images.

The present invention provides a method for generating a holographic image to generate multiple target images at different locations.

An embodiment of the present invention provides a method for generating a holographic image. The method includes: using a controller to generate multiple phase distributions corresponding to multiple target images; using the controller to superimpose the multiple phase distributions to obtain a phase-only mask; and inputting the phase-only mask. A spatial light modulator, so that the spatial light modulator expresses the phase-only mask; a light source is used to generate an illumination beam that is incident on the spatial light modulator, and the spatial light modulator converts the The illumination beam is converted into an image beam to generate multiple virtual images corresponding to the multiple target images, where the multiple virtual images are located at different locations in space.

Based on the above, the present invention can generate a single phase-only mask with different depths and different tilt angles to reconstruct multiple target images located at different depths, different tilt angles, and different offset distances.

FIG. 1 is a schematic diagram of an optical system according to an embodiment of the present invention. The optical system 10 is used to convert the illumination beam L into the image beam IB to form a plurality of virtual images V1 and V2. The optical system 10 includes a light source 100, a spatial light modulator 200, a controller 300, and a beam splitter 400.

The light source 100 in this embodiment is, for example, a laser diode (LD) light source, a light emitting diode (Light Emitting Diode, LED) light source, or other suitable light sources or combinations thereof. The light source 100 is used to emit the illumination beam L. The illumination beam L may be red light, green light, blue light or other colored light beams or a combination thereof.

The spatial light modulator 200 is disposed on the transmission path of the illumination beam L. The spatial light modulator 200 is, for example, a digital micro-mirror device (DMD), a silicon-based liquid crystal panel (liquid-crystal-on-silicon panel, LCOS panel), or any other optical element suitable for reconstructing a holographic image.

The controller 300 includes, for example, a microcontroller unit (MCU), a central processing unit (CPU), a microprocessor, a digital signal processor (DSP), a programmable The present invention is not limited to a controller, a programmable logic device (PLD) or other similar devices or a combination of these devices. In addition, in one embodiment, each function of the controller 300 may be implemented as multiple program codes. These program codes will be stored in a memory, and the controller 300 will execute these program codes. Alternatively, in one embodiment, each function of the controller 300 may be implemented as one or more circuits. The present invention is not limited to using software or hardware to implement each function of the controller 300 .

The method of generating a holographic image by the optical system 10 is as follows. The controller 300 is used to generate multiple phase distributions corresponding to multiple target images. The controller 300 is used to superimpose multiple phase distributions to obtain a phase-only mask. Then, the phase-only mask is input to the spatial light modulator 200, so that the spatial light modulator 200 represents the phase-only mask. The illumination beam L generated by the light source 100 is incident on the beam splitter 400, and the illumination beam is incident on the spatial light modulator 200, so that the illumination beam L is formed into an image beam IB to generate virtual images V1 and V2 corresponding to multiple target images. As shown in Figure 1, virtual images V1 and V2 are located at different locations in space. Through the phase-only mask generated by the controller 300, the optical system 10 can generate multiple different virtual images simultaneously.

The following describes how the controller 300 generates multiple phase distributions corresponding to multiple target images.

Figure 2 is an optical architecture diagram according to an embodiment of the present invention. Have phase-only masks on the input plane, with different phase distributions. When the illumination beam with wavelength λ is incident on the phase-only mask of the input plane (x ₀ , y ₀ , 0), it will be parallel to the reference plane (x, y, 0) through Fresnel transform The target image corresponding to the phase distribution of the phase-only mask is obtained on the output plane (x, y, z _i ). For example, through Fresnel transformation, one point on the input plane can be obtained The phase of the point on the output plane contribution.

1. Fresnel conversion

Fresnel conversion is introduced below.

Suppose there is a three-dimensional object with multiple target images arranged along the z direction and located at z=z _i , the total number is N, where i=1~N. each target image It can be expressed as formula (1): (1),

in as the target image Amplitude distribution in the output plane of z=z _i , as the target image Phase distribution on the output plane of z=z _i .

On the input plane, there are multiple target images corresponding to multiple original field signals , the total number is N, where i=1~N. Each original field signal It can be expressed as the following formula (2): (2),

The original field signal The intensity distribution at all positions is constant 1, which means that the original field signal only records the phase, where is the original field signal Phase distribution on the input plane at z=0.

When the incident light hits the input plane, the original field signal can be transformed into Generate the corresponding target image at z=z ₀ , as shown in equation (3):

in, The Fresnel transformation is calculated according to Equation (4):

Finally, for all target images By superimposing, you can get a complete total target image. , as shown in equation (5):

On the other hand, defining the total phase distribution on the input plane , so that the total phase distribution After Fresnel conversion, the total target image can be obtained , as shown in equation (6): Comparing formula (5) and formula (6), we can get formula (7):

It can be seen from equation (7) that the total phase distribution on the input plane is the sum of the input phases corresponding to each target image. Therefore, when incident light strikes an input plane with a total phase distribution, all target images are generated simultaneously.

The above is the basic principle of Fresnel conversion.

2. Calculate the phase distribution of the original field signal using a recursive algorithm

In order to obtain the target image corresponding to z=z _i on the input plane original field signal , or the original field signal The phase distribution of , so that the incident light has a phase distribution After combination, an image similar to the target image can be produced at z=z _i approximate target image , the present invention uses the following recursive algorithm to obtain the phase distribution located on the input plane.

The following explains how to use a recursive algorithm to find the target image corresponding to z=z _i original field signal The phase distribution of .

Figure 3 is a flowchart of a recursive algorithm according to an embodiment of the present invention.

Step 1: Generate an initial phase distribution and an initial amplitude on the input plane as the first phase distribution with the first amplitude distribution . The initial phase distribution is a randomly distributed phase . initial amplitude distribution The amplitude of is unit intensity 1, that is, the first amplitude distribution is a uniform intensity distribution. Distribute the first amplitude with the first phase distribution After multiplication, the input field signal is obtained or .

Step 2: Input field signal, i.e. first amplitude distribution with the first phase distribution The multiplied product is Fresnel transformed using equation (4) to obtain the approximate target image on the output plane at z=z _i , as shown in equation (8): Among them, the approximate target image The amplitude distribution of , phase distribution . will approximate the target image The amplitude distribution of As the second amplitude distribution , approximate target image The phase distribution of As the second phase distribution .

Step 3: Calculate approximate target image The amplitude distribution of (i.e. the second amplitude distribution) and the target image The amplitude distribution of The correlation coefficient (correlation coefficient), ρ, is shown in equation (9): where f ₁ and f ₂ are approximate target images respectively. The amplitude distribution of with target image The amplitude distribution of , and are the standard deviations of f ₁ and f ₂ respectively.

Step 4: If the target image is approximated The amplitude distribution of with target image The amplitude distribution of The correlation coefficient ρ is greater than or equal to a threshold value (for example, 0.9, but the present invention is not limited to this), then the first phase distribution as original field signal The phase distribution of , and end the algorithm, as shown in equation (10): (10).

Step 5: If the target image is approximated The amplitude distribution of with target image The amplitude distribution of The correlation coefficient ρ is less than the threshold (for example, 0.9, but the present invention is not limited to this), then the amplitude distribution of the target image As the third amplitude distribution , the second phase distribution As the third phase distribution , convert the third amplitude with third phase After multiplication, the inverse Fresnel transformation is performed, that is, , to obtain the fourth amplitude distribution located in the input plane and the fourth phase distribution .

Step 6: Distribute the fourth phase As the new first phase distribution , and set the first amplitude distribution The size is unit intensity, and repeat steps 2 to 6 until the target image is approximated The amplitude distribution of with target image The amplitude distribution of When the correlation coefficient ρ is greater than or equal to 0.9, the first phase distribution as original field signal The phase distribution of , or after repeating steps 2 to 6 for the preset number of times, use the first phase distribution as original field signal The phase distribution of .

According to the aforementioned recursive algorithm, the corresponding target images can be obtained in sequence original field signal The phase distribution of .

will correspond to each target image original field signal The phase distribution of superimposed to obtain the final total phase distribution , as shown in equation (11):

The total phase distribution obtained according to the above steps Also known as phase-only mask (POM), the controller causes the spatial light modulator to generate a phase distribution corresponding to the phase-only mask at the input plane position. When the incident light illuminates the spatial light modulator, When , a virtual image corresponding to the target image is generated at the output plane to achieve the projection effect.

3. Angle multi-tasking

The recursive algorithm mentioned above is applicable when the output plane and the input plane are parallel to each other, that is, the original field signal on the input plane and the target image on the output plane on the input plane parallel to each other, so the original field signal After Fresnel transformation, the target image on the output plane is obtained. .

When the original field signal on the input plane and the target image on the output plane When they are not parallel to each other, it is equivalent to viewing the target image located on the output plane from different viewing angles. At this time, the Fresnel conversion formula needs to be modified accordingly, that is, equation (4), so that the original field signal After Fresnel conversion, the output can be the same as the original field signal. Non-parallel target images .

3.1 Single axis rotation

The following takes a projection plane rotated by an angle around the x-axis as an example to illustrate how to calculate the phase signal on the input plane when the projection plane is not parallel to the input plane.

4 is an optical architecture diagram of Fresnel transformation of a tilted output plane according to an embodiment of the present invention. The geometric spatial relationship between the input plane, the reference plane, and the Fresnel diffraction of the output plane is shown in Figure 4.

In Figure 4, the input plane is the xy plane located at z=0. The reference plane is the xy plane located at z=z ₀ . The output plane is the reference plane centered at z=z ₀ and rotated by 𝜃 _igh along the x-axis direction. That is to say, after the reference plane is rotated by 𝜃 _igh along the x-axis direction at z=z ₀ , the output plane can be obtained.

Original field signal on the input plane After Fresnel transformation, the target image located on the tilted output plane can be obtained. .

A point on the tilted output plane Corresponds to a point on the input plane distance , as shown in equation (12):

in, Represents the angle of rotation of the output plane around the x- axis, The distance from the rotation center point to the center of the output plane for a tilted input plane.

Therefore, through equation (12), we can get the points on the input plane points on the output plane with an inclination distance relationship.

In order to make the original field signal on the input plane Can be Fresnel transformed to produce a target image located on an inclined output plane , replace equation (4) used in the Fresnel transformation of equation (8) in the recursive algorithm with equation (13), so that the original field signal on the input plane After Fresnel transformation, the target image located on the tilted output plane can be obtained. .

Corresponding to the rotation of the output plane 𝜃 _x about the x-axis, the modification of equation (4) in Fresnel transformation is as shown in equation (13):

Among them, 𝜆 is the wavelength, and z ₀ is the distance from the rotation center point of the tilted input plane to the center of the output plane.

In some embodiments, there may be N target images at z = z ₀ , i= 1 ~N , each image corresponds to a different tilt angle , through the aforementioned recursive algorithm and equation (13), the corresponding target image can be obtained on the input plane. phase signal , simplifying equation (13) into equation (14):

in for , i=1~𝑁 is the individual phase distribution after Fresnel transformation. Integrate individual phase distributions into a single phase distribution (Phase-only mask, POM), as shown in equation (15):

Therefore, when the angle difference between the output plane and the input plane of the target image is rotation around the x-axis, the Fresnel transformation can be calculated using Equation (13) to obtain the correct input phase distribution.

For example, FIG. 5 is a schematic diagram of reconstructing multiple target images with different tilt angles according to an embodiment of the present invention. In Figure 5, with 9 different tilt angles target image , where i=1-9. Corresponding to these target images , generate a phase-only mask POM on the input plane, so that all target images can be reconstructed after the incident light with wavelength λ passes through the POM. .

3.2 Double axial rotation

In addition to being rotated around the x-axis relative to the input plane, the target image can also have other tilt angles in some cases, such as rotating the x-axis and the y-axis simultaneously to obtain more output planes with different tilt angles. At this time, the rotation angle of the output plane relative to the reference plane can be decomposed into Euler rotations on the y-axis and the x-axis respectively. That is, the reference plane first rotates the y-axis θ _y , and then rotates the x-axis of the rotated reference plane. A rotation θ _x is performed to obtain an output plane with a specific tilt angle. 6 is an optical architecture diagram of Fresnel transformation of a tilted output plane according to an embodiment of the present invention. The geometric spatial relationship between the input plane, the reference plane, and the Fresnel diffraction of the output plane is shown in Figure 6.

Original field signal on the input plane After Fresnel transformation, the target image located on the tilted output plane can be obtained. .

A point on the tilted output plane Corresponds to a point on the input plane distance , as shown in equation (16):

in, Represents the angle of rotation of the output plane around the x- axis, Represents the angle of rotation of the output plane around the y- axis, The distance from the rotation center point to the center of the output plane for a tilted input plane. To simplify the notation, and can be recorded as .

Therefore, through equation (16), we can get the points on the input plane points on the output plane with an inclination distance relationship.

In order to make the original field signal on the input plane Can be Fresnel transformed to produce a target image located on an inclined output plane , replace equation (4) used in the Fresnel transformation of equation (8) in the recursive algorithm with equation (17), so that the original field signal on the input plane After Fresnel transformation, the target image located on the tilted output plane can be obtained. .

Correspondingly, the output plane is rotated by 𝜃 _x about the x-axis and rotated by 𝜃 _y about the y-axis. The modification of equation (4) in Fresnel transformation is as shown in equation (17):

Among them, 𝜆 is the wavelength, and z ₀ is the distance from the rotation center point of the tilted input plane to the center of the output plane.

In some embodiments, there may be N target images at z = z ₀ , i= 1 ~N , each image corresponds to a different tilt angle and (or), through the aforementioned recursive algorithm and equation (17), the corresponding target image can be obtained on the input plane. phase signal , simplify formula (17) into formula (18):

in for , i=1~𝑁 is the individual phase distribution after Fresnel transformation. Integrate individual phase components into a single phase distribution (Phase-only mask, POM), as shown in equation (19):

Therefore, when the angle difference between the output plane and the input plane of the target image is rotation around the x-axis and around the y-axis, equation (19) can be used to calculate the Fresnel transformation to obtain the correct input phase distribution.

For example, FIG. 7 is a schematic diagram of reconstructing multiple target images with different tilt angles according to an embodiment of the present invention. In Figure 7, with 9 different tilt angles target image , where i=1-9. Corresponding to these target images , generate a phase-only mask POM on the input plane, so that all target images can be reconstructed after the incident light with wavelength λ passes through the POM. .

4. Space multiplexing

The recursive algorithm mentioned above can simultaneously reconstruct multiple target images located at different depths z=z _i . But as mentioned earlier, all target images They are all located in the z-axis direction, so reconstructing multi-depth images on the same optical axis will cause the front and rear images to block each other.

FIG. 8 is a schematic diagram of multiple virtual images located at the same position in space and at different depths according to an embodiment of the present invention. The virtual image V1 and the virtual image V2 are respectively located on the same optical axis and at different depths. Therefore, when viewed from the z direction, there will be a problem of mutual occlusion between the two.

Therefore, one solution is to have each target image Produce displacements in the x-axis and y-axis directions respectively , so that the target image Translate to , so that target images located at different depths z _i to produce displacements in the x-axis and y-axis directions , to avoid mutual occlusion problems.

Calculate the target image corresponding to z=z _i on the input plane original field signal The method is as follows.

First, using the aforementioned recursive algorithm, calculate , target image at original field signal , get the original field signal The phase distribution of .

Then introduce the offset in the x-axis direction Offset from y-axis direction , to divide the phase distribution Tune into , so that the center position of the imaged target image can be displaced from (0,0) in the x-axis and y-axis directions to .

The phase distribution after each modulation superimposed to obtain the total phase distribution

The total phase distribution Perform Fresnel transformation to obtain N approximate target images ,i=1~N. Approximate target image Amplitude distribution and target image Calculate the correlation coefficient of the amplitude distribution. If the correlation coefficient is greater than a threshold, it is considered that the modulated phase distribution can produce the target image . If the correlation coefficient is less than a threshold, repeat the above steps until the correlation coefficient is greater than a threshold, or the number of repetitions exceeds a threshold.

Through the above algorithm, the target image can be Pan to , so that the target image located on the co-optical axis Produce displacement in the x-axis and y-axis directions In order to achieve the effect of being separated from each other, they will not overlap each other on the optical axis.

Figure 9 is a schematic diagram of a phase-only mask according to an embodiment of the present invention. Figure 10 is an image of multiple virtual images located at the same position in space and at different depths according to an embodiment of the present invention.

Please refer to both Figure 9 and Figure 10. The phase-only mask POM is the phase distribution of the target image bits before spatial multiplexing modulation. After being irradiated by incident light, multiple virtual images will block each other in space, making it impossible to clearly distinguish individual images.

FIG. 11 is a schematic diagram showing multiple virtual images located at different positions and at different depths in space according to an embodiment of the present invention. Figure 12 is an image of multiple virtual images located at different positions and different depths in space according to an embodiment of the present invention.

Please refer to both Figure 11 and Figure 12. After spatial multiplexing, the virtual images V1' and V2' are displaced on the x-axis and y-axis respectively. and , so that the generated virtual images can be separated, which is convenient for identifying each virtual image.

In addition, when applied to optical systems, such as dual-optical head-up displays, image deviation or deformation may occur due to tolerances during system assembly. Through spatial multiplexing and angle multiplexing, the image can be corrected without modifying the hardware, such as translation along the x-axis or y-axis, to obtain better display effects.

To sum up, the present invention can reconstruct a single phase-only mask with different depths and different tilt angles, and can achieve the simultaneous reconstruction of multi-depth projection heads-up displays with a single display system. It can effectively miniaturize the system and can Reduce the number of display units, effectively shrink the system size and reduce system costs.

10:Optical system

100:Light source

200: Spatial light modulator

300:Controller

400: Beam splitter

, , :Target image

IB: image beam

I ₀ : Target image amplitude distribution

I ₁ : first amplitude distribution

I ₂ : Second amplitude distribution

I ₃ : The third amplitude distribution

I ₄ : The fourth amplitude distribution

L: lighting beam

P, P’: point

POM: Phase Only Mask

r _x , r _xy : distance

V1, V2, V1’, V2’: virtual image

x ₀ , x, y ₀ , y, y', z: coordinate axis

z ₀ , z ₁ , z ₂ : distance

μ ₁ , ν ₁ , μ ₂ , ν ₂ : displacement

λ: wavelength

θ _x , θ _x1 , θ _x2 , θ x3 , θ _x4 , θ _{x5 ,} θ _x6 , θ _x7 , θ _x8 , θ _x9 , θ _xy , θ _xy1 , θ _xy2 , θ xy3 , θ _xy4 , θ _xy5 , _{θ xy6} , θ _xy7 , θ _xy8 , θ _xy9 : angle

Φ ₁ : First phase distribution

Φ ₂ : Second phase distribution

Φ ₃ : Third phase distribution

Φ ₄ : The fourth phase distribution

_φi : Phase distribution

FIG. 1 is a schematic diagram of an optical system according to an embodiment of the present invention. Figure 2 is an optical architecture diagram according to an embodiment of the present invention. Figure 3 is a flow chart of a recursive algorithm according to an embodiment of the present invention. 4 is an optical architecture diagram of Fresnel transformation of a tilted output plane according to an embodiment of the present invention. FIG. 5 is a schematic diagram of reconstructing multiple target images with different tilt angles according to an embodiment of the present invention. FIG. 6 is an optical architecture diagram of another Fresnel transformation of a tilted output plane according to an embodiment of the present invention. FIG. 7 is a schematic diagram of another method of reconstructing multiple target images with different tilt angles according to an embodiment of the present invention. FIG. 8 is a schematic diagram of multiple virtual images located at the same position in space and at different depths according to an embodiment of the present invention. Figure 9 is a schematic diagram of a phase only mask according to an embodiment of the present invention. Figure 10 is an image of multiple virtual images located at the same position in space and at different depths according to an embodiment of the present invention. FIG. 11 is a schematic diagram of multiple virtual images located at different positions and different depths in space according to an embodiment of the present invention. Figure 12 is an image of multiple virtual images located at different positions and different depths in space according to an embodiment of the present invention.

I ₀ : target image amplitude distribution

I ₁ : first amplitude distribution

I ₂ : Second amplitude distribution

I ₃ : The third amplitude distribution

I ₄ : The fourth amplitude distribution

Φ ₁ : First phase distribution

Φ ₂ : Second phase distribution

Φ ₃ : Third phase distribution

Φ ₄ : The fourth phase distribution

φ _i : phase distribution of the original field signal

Claims (9)

A method for generating a holographic image, including: using a controller to generate a corresponding phase distribution for each of multiple target images; using the controller to superimpose the multiple phase distributions to obtain a phase-only mask ; Input the phase-only mask into a spatial light modulator, so that the spatial light modulator represents the phase-only mask; use a light source to generate an illumination beam that is incident on the spatial light modulator, so The spatial light modulator converts the illumination beam into an image beam to generate multiple virtual images corresponding to the multiple target images, wherein the multiple virtual images are located at different locations in space. The method of claim 1, wherein the controller uses a recursive algorithm to generate the corresponding phase distribution for each of the plurality of target images, and the recursive algorithm includes: on the input The plane generates an initial phase distribution and an initial amplitude as the first phase distribution and the first amplitude distribution. The first amplitude distribution and the first phase distribution are multiplied to obtain an input field signal; the input field signal is processed Neel conversion is performed to obtain an approximate target image located on the output plane, using the amplitude distribution of the approximate target image as the second amplitude distribution, and using the phase distribution of the approximate target image as the second phase distribution; calculating the second amplitude The correlation coefficient between the distribution and the amplitude distribution of the target image; If the correlation coefficient is greater than a threshold, use the first phase distribution as the phase distribution of the target image on the input plane and end the recursive algorithm; if the correlation coefficient is less than the threshold, Taking the amplitude distribution of the target image as the third amplitude distribution and the second phase distribution as the third phase distribution, multiply the third amplitude distribution and the third phase distribution to obtain an inverse Fresnel Convert to obtain a fourth amplitude distribution and a fourth phase distribution located on the input plane; use the fourth phase distribution as a new first phase distribution, use the initial amplitude as a new initial amplitude, and repeat the iteration Backtracking algorithm. The method of claim 2, wherein the initial phase distribution is a randomly distributed phase, and the amplitude of the initial amplitude distribution is 1. The method of claim 2, wherein when the output plane is parallel to the input plane, the Fresnel transformation is performed on the input field signal to obtain the approximate target located on the output plane. The image can be expressed as:

Where g _i ( x ₀ , y ₀ ; 0) is the input field signal, G _i ( x , y ; z _i ) is the approximate target image, λ is the wavelength, z ₀ is the input plane center point to the output plane distance from the center point. The method of claim 2, wherein when the output plane is not parallel to the input plane, the Fresnel transformation is performed on the input field signal to obtain the approximation located on the output plane. The target image can be expressed as:

Where g( x0 _, y0 ) is the input field signal, Gx ( x',y' ) is the approximate target image, _{λ is} the wavelength, _z0 is the tilted input plane rotation center point to the output plane center _The distance between points, θ _x is the angle _of rotation of the output plane around the x- axis, _r distance. The method of claim 2, wherein when the output plane is not parallel to the input plane, the Fresnel transformation is performed on the input field signal to obtain the approximation located on the output plane. The target image can be expressed as:

Where g( x0 _, y0 ) is the input field signal, Gxy ( x',y' ) _is the approximate target image, λ is the wavelength _{, z0} is the tilted input plane rotation center point to the output plane center The distance between points, θ _x is the angle of rotation of the output plane around the x-axis, θ _y is the angle of _rotation of the output plane around the y- _axis , _r The distance between points ( x',y' ) on the output plane. The method of claim 2, wherein when the output plane is parallel to the input plane, the input field signal is modulated so that the center position of the approximate target image located on the output plane is (0,0) is shifted to (μ,ν). The method of claim 2, wherein calculating the correlation coefficient ρ between the second amplitude distribution and the amplitude distribution of the target image can be expressed as:

Where f ₁ is the second amplitude distribution, f ₂ is the amplitude distribution of the target image,

and

are the standard deviations of f ₁ and f ₂ respectively. The method as described in request item 2, wherein the threshold is 0.9.