Real-time quantitative phase detection device and method based on white light diffraction digital holography

Abstract

The invention discloses a real-time quantitative phase detection device and method based on white light diffraction digital holography, and belongs to the technical field of optical imaging. The device comprises a collimation light source, a light collecting mirror, an aperture diaphragm, a convergent lens diaphragm, a convergent lens, a polarizer, a polarization beam splitter prism, an achromatic wave plate, a tube lens, a microscope objective, a measured reflective object, a reflective concave grating, an analyzer, a spatial filter, a positive lens and a 3CMOS camera. The spatial filter is located between the analyzer and the positive lens. According to the method, a 3CMOS camera is adopted, three light intensity images of different channels are recorded at the same time, white light diffraction digital holography is used for real-time quantitative phase detection, spatial domain multiplexing is achieved through polarization regulation and control, through halo effect compensation and TIE-based direct phase demodulation, complex PU steps are omitted, complex amplitude distortion correction operation of DHM is avoided, and the method is suitable for large-scale industrial production. And the robustness of the real-time quantitative phase detection device is improved. According to the invention, high-precision and high-stability three-dimensional quantitative phase detection can be realized.

Description

Technical Field

[0001] This invention belongs to the field of optical imaging technology and relates to a real-time quantitative phase detection device and method based on white light diffraction digital holography. Background Technology

[0002] Quantitative phase microscopy (QPI) based on complex amplitude reconstruction benefits from its label-free and non-invasive nature, enabling high-precision and high-sensitivity quantitative phase imaging (QPI) of pure phase samples without the need for complex optical path structures. This overcomes the limitation of traditional optical microscopy, which relies heavily on intensity-contrast imaging and cannot obtain quantitative phase information from samples. Therefore, it has significant research value and application potential. Specifically, in the field of optical precision manufacturing, high-precision QPI of the surface shape and structure of micro-devices can serve as an important means of defect detection and quality assessment.

[0003] In the field of quantitative phase microscopy, both interferometric and non-interferometric imaging methods have their own strengths and face different challenges and opportunities. Furthermore, existing technologies still struggle with the limitations of traditional imaging methods in terms of computational efficiency, imaging modes, dynamic measurement, technology comparison and fusion, and structural optimization when facing flexible and varied measurement requirements.

[0004] In order to ensure the stability and high contrast of the interferogram, highly coherent light sources are widely used in QPI technology based on interferometry. However, this will cause the acquired wrap-around phase to be affected by crosstalk from noise such as Gaussian, speckle and discontinuity truncation, thereby reducing the measurement accuracy and spatiotemporal sensitivity of the system.

[0005] Compared to interferometric QPI, non-interferometric techniques suppress the influence of coherent noise by employing partially coherent or incoherent illumination. Among these, TIE-based non-interferometric QPI has attracted widespread attention because it eliminates the phase unwrapping (PU) step and enables direct imaging of absolute phase. Similar to other non-interferometric methods, TIE-based QPI typically requires expensive equipment or complex optical paths and correction algorithms.

[0006] Therefore, both interferometric and non-interferometric QPI technologies have room for optimization in improving the measurement accuracy and spatiotemporal sensitivity of the system. Through innovative structural design, a compact optical system can be established to achieve the comparison and complementary advantages of digital holography (DHM) and TIE technologies. Summary of the Invention

[0007] To address the problems of coherent noise crosstalk, complex phase unwrapping and iterative calculations, and halo effects in existing technologies, this invention aims to provide a real-time quantitative phase detection device and method based on white light diffraction digital holography. By applying white light diffraction digital holography to real-time quantitative phase detection and utilizing direct phase demodulation based on TIE, the complex PU step is eliminated, and the complex amplitude distortion correction operation of DHM is avoided, thus improving the robustness of the real-time quantitative phase detection device. This invention is applicable to the field of optical precision manufacturing and can achieve high-precision and high-stability three-dimensional quantitative phase detection.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] The real-time quantitative phase detection device based on white light diffraction digital holography disclosed in this invention includes a collimating light source, a condenser lens, an aperture stop, a converging lens stop, a converging lens, a polarizer, a polarizing beam splitter, and an achromatic light source. Waveplate, microscope lens, microscope objective, reflective object under test, reflective concave grating, analyzer, spatial filter, positive lens, 3CMOS camera. The polarizer is located to the left of the polarizing beam splitter prism, and the analyzer is located to the right. An achromatic... The waveplate is positioned above the tube mirror and below the polarizing beam splitter prism. Another achromatic... The waveplate is positioned below the reflective concave grating and above the polarizing beam splitter. The microscope objective is placed below the tube mirror. The spatial filter is located between the analyzer and the positive lens. A 3CMOS camera is used to acquire images generated by the interference of the object beam and the reference beam.

[0010] A collimated light source emits a parallel beam through a condenser lens, an aperture stop, a converging lens stop, and a converging lens. This beam passes through a polarizer to form linearly polarized light with an S-polarization state. After being reflected by a polarizing beam splitter, this S-polarized light passes through an achromatic lens... A waveplate converts the light into circularly polarized light. This circularly polarized light is converged by a microscope tube and then illuminated onto the surface of the reflective object being tested by the microscope objective. The light carrying the sample information is reflected by the sample and returns along the same path to the microscope objective, where it is then collimated into parallel light by the microscope tube. The circularly polarized light exiting the microscope tube is then subjected to an achromatic light exchange. The waveplate converts the light into linearly polarized light in the P-polarization state. This linearly polarized light then passes sequentially through a polarizing beam splitter and an achromatic beam splitter. A waveplate forms circularly polarized light in the P-polarization state, which is then incident on a reflective concave grating. Under the action of the concave grating, the incident P-polarized light forms a converging beam with multiple diffraction orders, which is focused at different positions on the focal plane of the reflective concave grating. After achromatic correction... The light is converted back to linearly polarized light in the S-polarization state after passing through the waveplate and returns to the polarizing beam splitter for reflection. The reflected S-polarized light then passes sequentially through an analyzer, a spatial filter located on the focal plane of the reflective concave grating, and finally a positive lens, forming two parallel beams with a spatial angle, which serve as the object beam and reference beam. The object beam and reference beam interfere with the target surface of the 3CMOS camera, forming a white light diffraction digital hologram, which is recorded by the camera.

[0011] After being diffracted by the concave reflection grating, the light beam forms a series of discrete converging beams of different diffraction orders in space due to the dispersion of the grating and the focusing characteristics of the concave surface. A spatial filter is positioned at the common focal plane of these converging beams. This spatial filter is a physical aperture with a passing aperture, comprising a slit and a pinhole array. By precisely adjusting the position of the spatial filter, its passing aperture is aligned with and allows only the two focal points of the 0th-order and +1st-order diffraction beams to pass through. The focal points of the remaining converging beams are blocked by the non-passing area of ​​the spatial filter. The 0th-order and +1st-order beams, filtered by the spatial filter, will begin to diverge again after passing through the filter aperture. Subsequently, the 0th-order and +1st-order diverging beams are incident on a positive lens. This positive lens is positioned so that its front focal plane approximately coincides with the plane of the spatial filter's passing aperture. According to the principles of geometric optics, when a point source is located on the front focal plane of the positive lens, its outgoing light will be converted into parallel light by the positive lens. Therefore, the two diverging beams originating from the 0th and +1st order focal points, respectively, are independently collimated into two parallel outgoing beams after passing through the positive lens. Since the 0th and +1st order beams originate from two spatially separated focal points on the focal plane of the spatial filter, and these two focal points have a specific lateral offset relationship with the optical axis of the positive lens, the two parallel beams produced after collimation by the same positive lens do not propagate in the same direction. They form a constant spatial angle determined by the separation distance between the two focal points and the focal length of the positive lens. The +1st order beam is the object beam, and the 0th order beam is the reference beam. These two parallel beams with a stable spatial angle are jointly guided to the imaging target area of ​​the 3CMOS camera. Because the two beams originate from the same light source and have high spatiotemporal coherence, interference occurs when the two beams meet on the camera target surface, forming stable spatial interference fringes, which are then recorded by the 3CMOS camera.

[0012] This invention discloses a real-time quantitative phase detection method based on white light diffraction digital holography, which performs real-time quantitative phase detection based on information recorded by the real-time quantitative phase detection system based on white light diffraction digital holography. The real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this invention includes the following steps:

[0013] Step 1: Reconstruct the +1 level spectrum diagrams corresponding to the three-channel intensity maps of the red (R), green (G), and blue (B) focused states from a single color digital hologram recorded by the 3CMOS camera.

[0014] The 3CMOS camera records the interference pattern on its target surface and outputs a color digital hologram. The hologram is a three-dimensional array at the data level, with each pixel... The information is composed of sub-pixel sensing values ​​corresponding to the wavelengths of red, green, and blue light, arranged and combined according to a specific color filter array. (Original data) It is the result of spatially tessellated mixing of the light intensity information from the R, G, and B spectral channels. Based on the precise arrangement rules of the color filter array embedded in the camera, from... The original sub-pixel data sets that record only red light intensity, only green light intensity, and only blue light intensity are identified and separated. Three two-dimensional intensity matrices with the same spatial resolution as the original hologram and perfectly aligned pixel positions are generated. , , This yields the desired monochrome three-channel image. A Fast Fourier Transform (FFT) is performed on each of the three single-channel images (R, G, and B). This transform converts the image from the spatial domain to the frequency domain, and the output is a complex matrix with the same size as each channel image, denoted as . , , ,in and The coordinates are in the frequency domain. The magnitude of this complex matrix intuitively represents the intensity distribution of different spatial frequency components in the image. A frequency shift is performed on the complex matrix by swapping its four quadrants. The zero-frequency component (i.e., the DC component) of the original spectrum is shifted from a corner position (usually the upper left corner) of the matrix to the geometric center of the spectrum. The spectrum after this processing is called the centered spectrum, with the central region representing low-frequency components and the periphery representing high-frequency components. This allows the carrier frequency component (represented as a symmetrical ±1 order spectrum) caused by the angle between the object light and the reference light to be more clearly identified outside the center of the spectrum. Then, in the centered spectrum of each channel, the corresponding +1 order spectrum is identified and extracted. In the amplitude distribution of the spectrum, bright spots with significantly concentrated energy are found, except for the central bright spot (corresponding to the zero-order spectrum, mainly containing DC and low-frequency background). According to the principle of off-axis holographic interference, these bright spots are symmetrically distributed on both sides of the center, corresponding to the -1 and +1 order spectra, respectively. +1 order spectrum specifically refers to the concentrated bright spot of energy located in a specific quadrant or direction predetermined according to the optical path layout. Its position can be predicted theoretically (based on known angles between the object beam and reference beam and system parameters) and precisely located in the actual spectrum by finding the region of local intensity maximum. A two-dimensional window function (usually a rectangular or circular window) is defined centered on the identified +1 order spectrum bright spot. Using this window function as a mask, only the spectral data within the window function's coverage area is retained on the centered complex spectrum matrix, while all spectral coefficients outside the window function region are set to zero. This operation completes the filtering and extraction of the +1 order spectral components. Subsequently, the extracted spectral data (a complex submatrix) is placed in the corresponding position of a new complex matrix with the same size as the original spectrum but all elements initially set to zero, thereby generating a new complex spectrum matrix containing only the target +1 order spectral information, denoted as . , , .

[0015] Step 2: Reconstruct the complex amplitude based on TIE to obtain the complex amplitude distribution of the reference light under different defocus states.

[0016] In the imaging optical path, the +1st order object light of the spatial filter is blocked, allowing only the 0th order reference light to illuminate the target surface of the 3CMOS camera, resulting in a single color reference light intensity image in the focused state. Following the aforementioned color image decoupling method, three monochromatic intensity images corresponding to the wavelengths of red, green, and blue light are separated from this color image, denoted as... , , These images directly reflect the two-dimensional intensity distribution of the reference light on the detector plane at different wavelengths. According to the relationship... The square of the reference light amplitude is proportional to its intensity distribution. Therefore, the amplitude term of the reference light in each channel... It can be obtained by calculating its intensity distribution.

[0017] The +1 order object light of the spatial filter is blocked, allowing only the 0th order reference light to illuminate the target surface of the 3CMOS camera. By moving the 3CMOS camera, reference light intensity maps under focused, overfocus, and underfocus states are acquired. Following the aforementioned color image decoupling method, monochrome images under focused, overfocus, and underfocus states in different channels are obtained. The phase is calculated using the TIE equation, and then...

[0018] Phase information of the R, G, and B channels is obtained. , , Finally, the amplitude term is combined with the phase information, and the complex amplitude of the reference light is reconstructed using a formula to obtain the complex amplitude distribution of the reference light under different defocus states.

[0019] Step 3: Using the reference optical complex amplitude obtained in Step 2, perform complex amplitude compensation on the +1 level spectral information of the focused state three-channel intensity map in Step 1.

[0020] Through formula ,in It is the +1st order sidelobe signal obtained in step one. It is the reference optical complex amplitude reconstructed from the TIE obtained in step two. It is the reference light intensity in the focused state. This represents the corrected sidelobe signal. It decouples the complex amplitudes of the object beam and the reference beam, obtaining the corrected +1-order spectral information for different channels.

[0021] Step 4: Using the spectral information of each channel after correction in Step 3, the corrected object light complex amplitude is reconstructed through the angular spectrum diffraction propagation algorithm, thus realizing real-time quantitative phase detection.

[0022] Using formula The corrected +1-order spectral information is multiplied by the angular spectral transfer function to obtain the corrected object beam angular spectrum for different channels. An inverse Fourier transform is then performed on the corrected angular spectrum to finally obtain the corrected object beam complex amplitude for different channels. , , .

[0023] Step 5: Propagate the compensated object light complex amplitudes obtained in Step 4 to the same spatial reference plane, extract the light intensity distribution on the plane, and use it for direct phase demodulation based on TIE.

[0024] The object light complex amplitude at the z=0 plane after R, G, and B channel compensation , , The complex amplitude distribution is transformed to the frequency domain using Fourier transform, yielding the angular spectra corresponding to the three channels. Using the angular spectrum transfer function mentioned in step four, it is propagated to the same spatial reference plane, which is parallel to the initial plane and separated from it by a propagation distance along the optical axis. By multiplying the initial plane z=0 angular spectrum by the angular spectrum transfer function of the corresponding channel using the formula, the propagated angular spectrum is obtained. The angular spectra of each channel at the plane. The propagated angular spectra are then transformed back into the spatial domain, ultimately obtaining the final result on the same spatial reference plane. The complex amplitude distribution of the three objects on the screen: : Red channel object optical complex amplitude. : Green channel optical recovery amplitude. Blue channel object optical complex amplitude. Using the formula... , The intensity distribution of the three channels on the same spatial plane was obtained. , , Then, the axial differential of light intensity is calculated using chromatic aberration, and the TIE equation is solved to obtain the phase. The calculated phase... The formula can be used to convert the actual height of the sample. This enables real-time quantitative phase demodulation based on white light diffraction digital holography, i.e., real-time quantitative phase detection.

[0025] The real-time quantitative phase detection method based on white light diffraction digital holography of the present invention requires numerical reconstruction of different complex amplitudes of multiple channels and propagation of the complex amplitudes to the same spatial position under different wavelength parameters. This allows a phase difference based on the principle of chromatic aberration to be generated between the complex amplitudes of different channels. This process simulates the difference in focusing state of intensity maps at different wavelengths in a white light image received by a single plane in space, due to the presence of chromatic aberration, which results in a phase difference.

[0026] The real-time quantitative phase detection method based on white light diffraction digital holography of the present invention records the color reference light intensity map under different focusing states by blocking the +1 stage aperture of the spatial filter in the wDPM structure and quantitatively adjusting the focusing state. The reference light intensity maps under three-channel focusing, under-focus, and over-focus are substituted into the TIE algorithm for calculation to obtain the phase matrix of the three-channel reference light.

[0027] Beneficial effects:

[0028] 1. The real-time quantitative phase detection device based on white light diffraction digital holography disclosed in this invention only requires one polarization beam splitter to split the beam into three, while the traditional method requires three beam splitters. Therefore, the system of this invention is more compact.

[0029] 2. The real-time quantitative phase detection device based on white light diffraction digital holography disclosed in this invention uses a 3CMOS camera to simultaneously record three light intensity images from different channels, and has the characteristics of good contrast and high spatial resolution.

[0030] 3. The real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this invention uses a spectrum compensation method to correct the sidelobe signals in the hologram spectrum information, thereby decoupling the complex amplitude of the object light and the reference light, effectively suppressing the halo effect and improving the measurement accuracy.

[0031] 4. The real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this invention eliminates the complex PU step by using direct phase demodulation based on TIE and avoids complex amplitude distortion correction operation of DHM, thereby improving the robustness of the real-time quantitative phase detection device.

[0032] 5. The real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this invention realizes real-time quantitative phase detection based on the point diffraction structure. It is easy to assemble and adjust, has high accuracy, and can improve the stability and anti-interference ability of the real-time quantitative phase detection device. Attached Figure Description

[0033] Figure 1 A schematic diagram of the real-time quantitative phase detection device based on white light diffraction digital holography of the present invention;

[0034] Wherein: 1—collimating light source, 2—light collector, 3—aperture stop, 4—converging lens stop, 5—converging lens, 6—polarizer, 7—polarizing beam splitter, 8—achromatic light source 9—wave plate, 10—microscope objective, 11—reflective object under test, 12—achromatic 13—Wave plate, 14—Reflective concave grating, 15—Analyzer, 16—Spatial filter, 17—Positive lens, 18—3CMOS camera.

[0035] Figure 2 A schematic diagram of the beam splitting characteristics of the polarization beam splitter prism 7 of the real-time quantitative phase detection device based on white light diffraction digital holography of the present invention.

[0036] Figure 3 A schematic flowchart of the real-time quantitative phase detection method based on white light diffraction digital holography of the present invention.

[0037] Figure 4 The present invention provides an example of the real-time quantitative phase detection device based on white light diffraction digital holography used to measure micro / nano devices. Figure (a) shows the quantitative phase detection result of the micro / nano device (with a halo), and Figure (b) shows the quantitative phase detection result of the micro / nano device (without a halo). Detailed Implementation

[0038] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0039] Example 1:

[0040] like Figure 1 As shown, the real-time quantitative phase detection device based on white light diffraction digital holography disclosed in this embodiment includes a polarizer 6, a polarizing beam splitter 7, an analyzer 14, a spatial filter 15, a positive lens 16, a 3CMOS camera 17, a microscope objective 10, a tube mirror 9, and an achromatic microscope. Wave plate 8, achromatic Wave plate 12, reflective concave grating 13.

[0041] like Figure 1 As shown, the polarizer 6 and the analyzer 14 are located on the left and right sides of the polarizing beam splitter 7, respectively; the spatial filter 15 is located between the analyzer 14 and the positive lens 16.

[0042] like Figure 1 As shown, the achromatic color difference Wave plate 8, achromatic Waveplate 12 uses the same model. Its achromatic characteristics are designed to ensure that light of different wavelengths can converge at the same spatial position and to achieve the control of the polarization state of the light.

[0043] like Figure 1 As shown, the spatial filter 15 is located on the back focal plane of the reflective concave grating 13, and the spatial filter 15 only allows the +1st and 0th order beams to pass through, which serve as the object beam and reference beam respectively, while the other orders are completely blocked.

[0044] like Figure 2 As shown, the polarization beam splitter 7 is used to realize polarization-based spatial multiplexing and to enable the optical path to complete full optical path propagation within it.

[0045] like Figure 1 As shown, the real-time quantitative phase detection device based on white light diffraction digital holography disclosed in this embodiment first passes a parallel beam emitted by a white LED illumination system through a polarizer 6 to form linearly polarized light in an S-polarization state; after being reflected by a polarizing beam splitter prism 7, the S-polarized light passes through an achromatic... Waveplate 8 converts the light into circularly polarized light; subsequently, this circularly polarized light is converged by tube lens 9 and then illuminated onto the object surface by microscope objective 10; the light carrying the object's information is reflected by the object and returns to microscope objective 10 along the same path, and is then collimated into parallel light by tube lens 9; the circularly polarized light exiting tube lens 9 is then achromatic again... Waveplate 8 converts the light into linearly polarized light in the P-polarization state. This linearly polarized light then passes sequentially through polarizing beam splitter 7 and achromatic beam splitter 7. Waveplate 12 forms circularly polarized light in the P-polarization state, which is then incident on a reflective concave grating 13. Under the action of the concave grating 13, the incident P-polarized light forms a converging beam with multiple diffraction orders, which is focused at different positions on the focal plane of the reflective concave grating 13, and then achromatic. After waveplate 12, the light is converted back into linearly polarized light in the S-polarization state and returns to the polarization beam splitter 7 for reflection. The reflected S-polarized light passes sequentially through the analyzer 14 and the spatial filter 15 located on the focal plane of the reflective concave grating 13. Then, through the action of the positive lens 16, two parallel beams with a spatial angle are formed. The spatial filter 15 only allows the +1st and 0th order beams to pass through, which serve as the object beam and reference beam, respectively, while the other orders are completely blocked. Finally, the object beam and the reference beam interfere on the target surface of the 3CMOS camera 17 to form a white light diffraction digital hologram, which is recorded by the camera.

[0046] like Figure 3 As shown, the real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this embodiment performs real-time quantitative phase detection based on the information recorded by the real-time quantitative phase detection method based on white light diffraction digital holography. The specific implementation steps of the real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this embodiment are as follows:

[0047] Step 1: Reconstruct the +1 level spectrograms corresponding to the red (R), green (G), and blue (B) channels from a single color digital hologram.

[0048] First, after recording the color off-axis digital hologram, three single-channel images are obtained. Then, fast Fourier transform is performed on the R, G, and B single-channel images respectively to convert the images from the spatial domain to the frequency domain and perform frequency shift. Finally, the corresponding +1 level spectrum is identified and extracted from the spectrum of each channel.

[0049] Step 2: Reconstruct the complex amplitude based on TIE to obtain the complex amplitude distribution of the reference light in different defocus states (including focused, underfocus, and overfocus). First, construct the amplitude term from the reference light intensity map in the focused state; then, use TIE to solve the phase of the light intensity maps in different defocus states obtained in the R, G, and B channels; finally, combine the constructed amplitude term with the phase information obtained from TIE to reconstruct the complex amplitude of the reference light.

[0050] Step 3: Using the reference optical complex amplitude obtained in Step 2, perform complex amplitude compensation on the +1 level spectrum of the focused state three-channel intensity map in Step 1.

[0051] The sidelobe signals in the spectral information are corrected by using the reference optical complex amplitude, thereby decoupling the object light and the reference optical complex amplitude and obtaining the corrected +1 level spectral information.

[0052] Step 4: Reconstruct the corrected object light complex amplitude using the angular spectrum diffraction propagation algorithm based on the spectral information of each channel after correction in Step 3.

[0053] The angular spectrum information is converted back to the spatial domain by performing an inverse Fourier transform on the corrected +1 level spectral information, and the distribution of the complex amplitude of the object light is obtained under the action of the angular spectrum transfer equation.

[0054] Step 5: Propagate the compensated object light complex amplitude of each channel to the same spatial plane, extract the light intensity distribution on the plane, and use it for TIE-based direct phase demodulation.

[0055] First, the object light complex amplitude after compensation for all channels (R, G, B) needs to be propagated to the same reference plane; then, the light intensity distribution of each channel on the plane is calculated to obtain the three-channel light intensity distribution on the same spatial plane; finally, the axial differential of the light intensity is calculated through the resulting color difference, and the TIE equation is solved to achieve direct phase adjustment of the digital hologram.

[0056] Example 2:

[0057] like Figure 1 As shown, the real-time quantitative phase detection device based on white light diffraction digital holography disclosed in this embodiment includes a collimating light source 1, a condenser lens 2, an aperture stop 3, a converging lens stop 4, a converging lens 5, a polarizer 6, a polarizing beam splitter 7, and an achromatic light source 8. 8. Wave plate; 9. Tube endoscope; 10. Microscope objective; 11. Reflective object under test; achromatic. Waveplate 12, reflective concave grating 13, analyzer 14, spatial filter 15, positive lens 16, 3CMOS camera 17. Polarizer 6 and analyzer 14 are located on the left and right sides of polarizing beam splitter 7, respectively. An achromatic... Waveplate 8 is located above tube mirror 9 and below polarizing beam splitter 7. Another achromatic... Waveplate 12 is located below reflective concave grating 13 and above polarizing beam splitter 7. Microscope objective 10 is positioned below tube mirror 9. Spatial filter 15 is located between analyzer 14 and positive lens 16. 3CMOS camera 17 is used to acquire images generated by the interference of object beam and reference beam.

[0058] like Figure 4 As shown, Figure (a) is a quantitative phase detection result of the micro-nano device obtained by the real-time quantitative phase detection device based on white light diffraction digital holography. The halo effect (blue area) is obvious in the image, and there is a depression.

[0059] A collimated light source 1 (440-670nm, 3W) emits a parallel beam through a condenser lens 2 (25mm), an aperture stop 3, a converging lens stop 4, and a converging lens 5 (75mm). This beam first passes through a polarizer 6 to form linearly polarized light in an S-polarization state. This S-polarized light is then reflected by a polarizing beam splitter prism 7 (420-680nm, Tp>90%, Rs>99.5%) and passes through an achromatic... Waveplate 8 converts the light into circularly polarized light. This circularly polarized light is then converged by tube lens 9 (200 mm, 350-700 nm) and passed through the microscope objective. The light is irradiated onto the surface of the reflective object 11 being tested. The light carrying the sample information is reflected by the sample and returns along the same path to the microscope objective 10, where it is then collimated into parallel light by the tube lens 9. The circularly polarized light exiting from the tube lens 9 then passes through an achromatic lens... Waveplate 8 converts the light into linearly polarized light in the P-polarization state. This linearly polarized light then passes sequentially through polarizing beam splitter 7 and achromatic beam splitter 7. Waveplate 12 forms circularly polarized light in the P-polarization state, which is then incident on a reflective concave grating 13. Under the action of the concave grating 13, the incident P-polarized light forms a converging beam with multiple diffraction orders, which is focused at different positions on the focal plane of the reflective concave grating 13, and then achromatic... After passing through waveplate 12, the light is converted back to linearly polarized light in the S-polarization state and returns to the polarizing beam splitter prism 7 for reflection. The reflected S-polarized light then passes sequentially through analyzer 14, spatial filter 15 (Φ25.4mm) located on the focal plane of the reflective concave grating 13, and then through positive lens 16 (50mm), forming two parallel beams with a spatial angle, which serve as the object beam and reference beam. The object beam and reference beam interfere with the target surface of the 3CMOS camera 17 (5480×3648, 390nm-650nm, 1.64W), forming a white light diffraction digital hologram, which is recorded by the camera.

[0060] The concave reflective grating 13 integrates both beam splitting and focusing functions. The surface of the grating 13 is engraved with numerous parallel, equally spaced grooves. An incident beam containing multiple wavelengths, according to the grating equation, has different diffraction angles for different wavelengths at the same incident angle, thus separating them spatially according to wavelength (color). The light diffracts on the grooves. Due to the grating's dispersion and the concave focusing characteristics, a series of discrete converging beams of different diffraction orders (e.g., ...-2, -1, 0, +1, +2, ...) are formed in space. A spatial filter 15 is positioned at the common focal plane of these converging beams. This spatial filter 15 is typically a physical aperture (e.g., a slit or pinhole array) with a specific aperture. By precisely adjusting the position of the spatial filter 15, its aperture is aligned only with and allows the two focal points of the 0th-order and +1st-order diffraction beams to pass through. The focal points of the remaining converging beams are blocked by the non-transparent area of ​​the spatial filter 15. The two beams of light, 0th and +1st order, that pass through the spatial filter 15 will begin to diverge again after passing through the filter aperture. These two diverging beams are then incident on a positive lens 16. The positive lens 16 is positioned so that its front focal plane approximately coincides with the aperture plane of the spatial filter 15. According to the principles of geometric optics, when a point source is located on the front focal plane of the positive lens 16, its outgoing light will be converted into parallel light by the lens 16. Therefore, the two diverging beams originating from the 0th and +1st order focal points are independently collimated into two parallel outgoing beams after passing through the positive lens. Since the 0th and +1st order beams originate from two spatially separated focal points on the focal plane of the spatial filter 15, and these two focal points have a specific lateral offset relationship with the optical axis of the positive lens 16, the two parallel beams produced after collimation by the same positive lens 16 do not propagate in the same direction. They form a constant spatial angle determined by the distance between the two focal points and the focal length of the positive lens 16. One beam (+1 order) is the object beam, and the other (0 order) is the reference beam. Ultimately, these two parallel beams (object beam and reference beam) with a stable spatial angle are guided together to the imaging target area of ​​the 3CMOS camera 17. Because they originate from the same light source and possess high spatiotemporal coherence, they interfere when they meet on the camera target surface, forming stable spatial interference fringes, which are then recorded by the 3CMOS camera 17.

[0061] The real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this embodiment performs real-time quantitative phase detection based on the information recorded by the real-time quantitative phase detection method based on white light diffraction digital holography. The specific implementation steps of the real-time quantitative phase detection method based on white light diffraction digital holography disclosed in this embodiment are as follows:

[0062] Step 1: Reconstruct the +1 level spectrograms of the three channels (Red R, Green G, and Blue B) from a single color digital hologram recorded by the 3CMOS camera 17.

[0063] The 3CMOS camera 17 records the interference pattern on its target surface and outputs a color digital hologram. The hologram is a three-dimensional array at the data level, with each pixel... The information is composed of sub-pixel sensing values ​​corresponding to the wavelengths of red, green, and blue light, arranged and combined according to a specific color filter array. Therefore, the original data Essentially, it's the result of spatially tessellated mixing of the light intensity information from the R, G, and B spectral channels. Based on the precise arrangement rules of the color filter array embedded in the camera, from... The original sub-pixel data sets that record only red light intensity, only green light intensity, and only blue light intensity are identified and separated, generating three two-dimensional light intensity maps with the same spatial resolution as the original hologram and perfectly aligned pixel positions. , , This refers to a monochrome three-channel image. A Fast Fourier Transform (FFT) is performed on each of the three single-channel images (R, G, and B). This transform converts the image from the spatial domain to the frequency domain, and the output is a complex matrix with the same size as each channel image, denoted as [matrix name missing]. , , , where u and v are frequency domain coordinates. The magnitude of this complex matrix intuitively represents the intensity distribution of different spatial frequency components in the image. Frequency shifting is then performed, achieved by swapping the four quadrants of the complex matrix. The zero-frequency component (i.e., the DC component) of the original spectrum is shifted from a corner position (usually the upper left corner) of the matrix to the geometric center of the spectrum. The spectrum after this processing is called the centered spectrum, with the central region representing low-frequency components and the periphery representing high-frequency components, allowing the carrier frequency component (represented as a symmetrical ±1 order spectrum) caused by the angle between the object light and the reference light to be more clearly identified outside the center of the spectrum. Then, in the centered spectrum of each channel, the corresponding +1 order spectrum is identified and extracted. In the amplitude distribution of the spectrum, bright spots with significantly concentrated energy are searched, excluding the central bright spot. According to the principle of off-axis holographic interference, these bright spots are symmetrically distributed on both sides of the center, corresponding to the -1 order and +1 order spectra, respectively. The +1 order spectrum specifically refers to the bright spot with concentrated energy located in a specific quadrant or direction predetermined according to the optical path layout. Its location can be predicted theoretically (based on the known angle between the object beam and the reference beam and system parameters) and precisely located in the actual spectrum by finding the region of local intensity maximum. A two-dimensional window function (usually a rectangular or circular window) is defined centered on the identified +1-order spectral bright spot. Using this window function as a mask, only the spectral data within the window function's coverage area is retained on the centered complex spectral matrix, while all spectral coefficients outside the window function region are set to zero. This operation completes the filtering and extraction of the +1-order spectral components. Subsequently, the extracted spectral data (a complex submatrix) is placed in the corresponding position of a new complex matrix with the same size as the original spectrum but all elements initially set to zero, thus generating a new complex spectral matrix containing only the target +1-order spectral information, denoted as . , , Performing an inverse Fast Fourier Transform on the image transforms it from the frequency domain to the spatial domain, yielding the corresponding +1 level spectrogram. , , .

[0064] Step 2: Reconstruct the complex amplitude based on TIE to obtain the complex amplitude distribution of the reference light under different defocus states.

[0065] In the imaging optical path, the +1st order object light of the spatial filter 15 is blocked, allowing only the 0th order reference light to illuminate the target surface of the 3CMOS camera 17, thus obtaining a single color reference light intensity map in the focused state. Following the aforementioned color image decoupling method, three monochromatic intensity images corresponding to the wavelengths of red, green, and blue light, respectively, are extracted from the color image, denoted as... , , These images directly reflect the two-dimensional intensity distribution of the reference light on the detector plane at different wavelengths. According to the relationship... The square of the reference light amplitude is proportional to its intensity distribution. Therefore, the amplitude term of the reference light in each channel... Its intensity distribution can be obtained by performing the following calculation:

[0066]

[0067]

[0068]

[0069] The +1st order object light of the spatial filter 15 is blocked, allowing only the 0th order reference light to illuminate the target surface of the 3CMOS camera 17. By moving the 3CMOS camera 17, reference light intensity maps under focused, overfocus, and underfocus states are acquired. Following the aforementioned color image decoupling method, monochrome images under focused, overfocus, and underfocus states in different channels are obtained. According to the TIE equation...

[0070]

[0071] Among them, the axial differential of light intensity on the left side of TIE Typically, the difference between reference intensity maps acquired from different channels under focused, over-focused, and under-focused states is used to represent the intensity. In the formula, , , These are reference light intensity diagrams for underfocus, focused, and overfocus conditions, respectively. Represents the distance between the focal plane and the focal plane. This represents the distance between the focused and underfocused planes. The calculated phase expression is:

[0072]

[0073] In the formula, Representing the two-dimensional Fourier transform and the two-dimensional inverse Fourier transform, k is a constant value, and u and v are the frequency domain coordinates corresponding to x and y, thus obtaining the reference light phase information in the R, G, and B channels. , , .

[0074] The amplitude term is combined with phase information and used in the formula

[0075]

[0076]

[0077]

[0078] The complex amplitude of the reference light is reconstructed, and the complex amplitude distribution of the reference light under different defocus states is obtained.

[0079] Step 3: Using the reference optical complex amplitude obtained in Step 2, perform complex amplitude compensation on the +1 level spectral information of the focused state three-channel intensity map in Step 1.

[0080] Through formula ,in The +1 order sidelobe signal obtained in step one, It is the reference optical complex amplitude reconstructed from the TIE obtained in step two. It is the reference light intensity in the focused state. This represents the corrected sidelobe signal. It decouples the complex amplitudes of the object beam and the reference beam, obtaining the corrected +1-order spectral information for different channels. , , .

[0081] Step 4: Using the spectral information of each channel after correction in Step 3, reconstruct the corrected object light complex amplitude using the angular spectrum diffraction propagation algorithm.

[0082] Using formula in, It is the corrected +1 level spectral information, and the angular spectral transfer function. Multiplying these results in the corrected object angular spectra for different channels. Among them, the angular spectrum transfer function , , These are the coordinates in two directions in the frequency domain. It is the actual propagation distance from the sample surface to the imaging surface. It is the center wavelength of the illumination source. (Regarding the corrected angular spectrum) Perform inverse Fourier transform Obtain the corrected object optical complex amplitude in different channels , , .

[0083] Step 5: Propagate the compensated object light complex amplitudes obtained in Step 4 to the same spatial reference plane, extract the light intensity distribution on the plane, and use it for direct phase demodulation based on TIE.

[0084] The object light complex amplitude at the z=0 plane after R, G, and B channel compensation , , Using Fourier transform Transform its complex amplitude distribution to the frequency domain to obtain the angular spectrum corresponding to the three channels. , , . To the initial planar spatial coordinates The corresponding spatial frequency coordinates. Using the angular spectral transfer function mentioned in step four. This propagates the light to the same spatial reference plane z=D, which is parallel to the initial plane and is separated from the propagation plane by a distance along the optical axis. The center wavelength corresponding to each channel is known, denoted as . , , Through the formula Multiplying the initial plane z=0 angular spectrum with the angular spectrum transfer function of the corresponding channel yields the angular spectrum of each channel at the propagated z=D plane. , , .pass Transforming the propagated angular spectrum back into the spatial domain ultimately yields the complex amplitude distributions of the three object beams on the same spatial reference plane z=D: , , In the formula, This represents the two-dimensional discrete inverse Fourier transform operator. Then, using the formula... , The intensity distribution of the three channels at z=D on the same spatial plane was obtained. , , .

[0085] Calculate the axial differential of light intensity using color difference:

[0086]

[0087] In the formula, This represents the equivalent image plane propagation distance from the R or B channel to the G channel, and This represents the light intensity difference from the R or B channel to the G channel.

[0088] According to the solution Substituting into the TIE equation,

[0089]

[0090] The phase expression obtained by solving is:

[0091]

[0092] In the formula, Representing the two-dimensional Fourier transform and the two-dimensional inverse Fourier transform, k is a constant value, and u, v are the frequency domain coordinates corresponding to x and y. Based on the calculated phase... pass Converted to the actual height of the sample .

[0093]

[0094] Real-time quantitative phase demodulation based on white light diffraction digital holography is achieved.

[0095] like Figure 4 As shown in Figure (b), the quantitative phase detection result of the micro-nano device obtained by the real-time quantitative phase detection method based on white light diffraction digital holography is shown in Figure (b). After processing by the method, the blue area in Figure (b) basically disappears, the halo effect is significantly suppressed, and high-precision and high-stability three-dimensional quantitative phase detection is achieved.

[0096] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A real-time quantitative phase detection device based on white light diffraction digital holography, characterized in that: Includes collimating light source, condenser lens, aperture stop, converging lens stop, converging lens, polarizer, polarizing beam splitter, and achromatic light source. Waveplate, tube mirror, microscope objective, reflective object under test, reflective concave grating, analyzer, spatial filter, positive lens, 3CMOS camera; polarizer is located on the left side of polarizing beam splitter, analyzer is located on the right side of polarizing beam splitter; an achromatic... The waveplate is positioned above the tube mirror and below the polarizing beam splitter prism; another achromatic... The waveplate is located below the reflective concave grating and above the polarizing beam splitter; the microscope objective is placed below the tube mirror; the spatial filter is located between the analyzer and the positive lens; and the 3CMOS camera is used to acquire images generated by the interference of the object beam and the reference beam.

2. The apparatus as described in claim 1, characterized in that: A collimated light source emits a parallel beam through a condenser lens, an aperture stop, a converging lens stop, and a converging lens. This beam passes through a polarizer to form linearly polarized light with an S-polarization state. After being reflected by a polarizing beam splitter, this S-polarized light passes through an achromatic lens. A waveplate converts the light into circularly polarized light; this circularly polarized light is converged by a microscope tube and then illuminated onto the surface of the reflective object being tested by the microscope objective; the light carrying the sample information is reflected by the sample and returns to the microscope objective along the same path, where it is then collimated into parallel light by the microscope tube; the circularly polarized light exiting the microscope tube is then further collimated by an achromatic microscope. The waveplate converts the light into linearly polarized light in the P-polarization state. This linearly polarized light then passes sequentially through a polarizing beam splitter and an achromatic beam splitter. A waveplate forms circularly polarized light in the P-polarization state, which is then incident on a reflective concave grating. Under the action of the concave grating, the incident P-polarized light forms a converging beam with multiple diffraction orders, which is focused at different positions on the focal plane of the reflective concave grating. After achromatic correction... After being converted back to S-polarized linearly polarized light by the waveplate, the light returns to the polarization beam splitter and is reflected. The reflected S-polarized light then passes sequentially through an analyzer, a spatial filter located on the focal plane of the reflective concave grating, and then through a positive lens to form two parallel beams with a spatial angle, which serve as the object beam and the reference beam. The object beam and the reference beam interfere with the target surface of the 3CMOS camera to form a white light diffraction digital hologram, which is recorded by the camera.

3. The apparatus as described in claim 1, characterized in that: After the light beam is diffracted by the concave reflection grating, due to the dispersion of the grating and the focusing characteristics of the concave surface, a series of discrete converging beams of different diffraction orders are formed in space. A spatial filter is placed at the common focal plane of these converging beams. This spatial filter is a physical aperture with a light-transmitting aperture, including a slit and a pinhole array. By precisely adjusting the position of the spatial filter, its light-transmitting aperture is aligned with and allows only the two focal points of the 0th-order and +1st-order diffraction beams to pass through. The focal points of the other orders of converging beams are blocked by the non-light-transmitting area of ​​the spatial filter. The 0th-order and +1st-order beams that have passed through the spatial filter will begin to diverge again after passing through the filter aperture. Subsequently, the 0th-order and +1st-order diverging beams are incident on a positive lens. This positive lens is placed at a position where its front focal plane approximately coincides with the light-transmitting aperture plane of the spatial filter. According to the principles of geometric optics, when a point source is located on the front focal plane of the positive lens, its output... The emitted light is converted into parallel light by the positive lens; therefore, the two diverging beams originating from the 0th order and +1st order focal points, respectively, are independently collimated into two parallel outgoing beams after passing through the positive lens. Since the 0th order and +1st order beams originate from two spatially separated focal points on the focal plane of the spatial filter, and the two focal points have a specific lateral offset relationship with the optical axis of the positive lens, the two parallel beams produced after collimation by the same positive lens do not have the same propagation direction; they form a constant spatial angle between them, which is determined by the separation distance between the two focal points and the focal length of the positive lens; the +1st order beam is the object beam, and the 0th order beam is the reference beam; the two parallel beams with a stable spatial angle are jointly guided to the imaging target area of ​​the 3CMOS camera; since the two beams come from the same light source and have high spatiotemporal coherence, when the two beams meet on the camera target surface, they will interfere, forming stable spatial interference fringes, which are then recorded by the 3CMOS camera.

4. A method for real-time quantitative phase detection based on information recorded by the device according to claim 1, characterized in that: Includes the following steps, Step 1: Reconstruct the +1 level spectrum diagrams corresponding to the three-channel intensity maps of the red (R), green (G), and blue (B) focused states from a single color digital hologram recorded by the 3CMOS camera. The 3CMOS camera records the interference pattern on its target surface and outputs a color digital hologram. ; The hologram is a three-dimensional array at the data level, with each pixel... The information is composed of sub-pixel sensing values ​​corresponding to the wavelengths of red, green, and blue light, arranged and combined according to a specific color filter array; raw data It is the result of spatially tessellated mixing of the light intensity information from the R, G, and B spectral channels; based on the precise arrangement rules of the color filter array embedded in the camera, from The original sub-pixel data sets that record only red light intensity, only green light intensity, and only blue light intensity are identified and separated; three two-dimensional intensity matrices with the same spatial resolution as the original hologram and perfectly aligned pixel positions are generated. , , This is the desired monochrome three-channel image. Fast Fourier Transform (FFT) is performed on the three single-channel images R, G, and B respectively. This transform converts the image from the spatial domain to the frequency domain, and the output is a complex matrix with the same size as each channel image, denoted as [matrix name missing]. , , ,in and The coordinates are in the frequency domain. The magnitude of this complex matrix intuitively represents the intensity distribution of different spatial frequency components in the image. The complex matrix is ​​frequency-shifted by swapping its four quadrants. The zero-frequency component of the original spectrum is shifted from the corner of the matrix to the geometric center of the spectrum. The spectrum after this processing is called the centered spectrum, with the central region representing low-frequency components and the periphery representing high-frequency components. This makes the carrier frequency component caused by the angle between the object light and the reference light more clearly identifiable around the center of the spectrum. Then, in the centered spectrum of each channel, the corresponding +1 level spectrum is identified and extracted. In the amplitude distribution of the spectrum, bright spots with significantly concentrated energy are found, except for the central bright spot. According to the off-axis holographic interference principle, the bright spots are symmetrically distributed on both sides of the center, corresponding to the -1 level and +1 level spectra, respectively. The +1 level spectrum specifically refers to the bright spot with concentrated energy located in a quadrant or direction predetermined according to the optical path layout. Its location is predicted based on the known angle between the object beam and the reference beam, as well as system parameters, and is precisely located in the actual spectrum by finding the region of local intensity maximum. A two-dimensional window function is defined centered on the identified +1-order spectral bright spot. Using this two-dimensional window function as a mask, only the spectral data within the window function's coverage area is retained on the centered complex spectrum matrix, while all spectral coefficients outside the window function region are set to zero. This operation completes the filtering and extraction of the +1-order spectral components. Subsequently, the extracted spectral data is placed in the corresponding position of a new complex matrix with the same size as the original spectrum but all elements initially set to zero, thereby generating a new complex spectrum matrix containing only the target +1-order spectral information, denoted as […]. , , ; Step 2: Reconstruct the complex amplitude based on TIE to obtain the complex amplitude distribution of the reference light under different defocus states; Step 3: Using the reference optical complex amplitude obtained in Step 2, perform complex amplitude compensation on the +1 level spectral information of the focused state three-channel intensity map in Step 1; Step 4: Using the spectral information of each channel after correction in Step 3, reconstruct the corrected object beam complex amplitude using the angular spectrum diffraction propagation algorithm; Step 5: Propagate the compensated object light complex amplitude obtained in Step 4 to the same spatial reference plane, extract the light intensity distribution on the plane, and use it for direct phase demodulation based on TIE, that is, realize real-time quantitative phase detection.

5. The method as described in claim 4, characterized in that: The second step is implemented as follows: In the imaging optical path, the +1st order object light of the spatial filter is blocked, allowing only the 0th order reference light to illuminate the target surface of the 3CMOS camera, resulting in a single color reference light intensity image in the focused state. Following the aforementioned color image decoupling method, three monochromatic intensity images corresponding to the wavelengths of red, green, and blue light are separated from this color image, denoted as... , , These images directly reflect the two-dimensional intensity distribution of the reference light on the detector plane at different wavelengths; according to the relationship... The square of the reference light amplitude is proportional to its intensity distribution; therefore, the amplitude term of the reference light in each channel... It is obtained by calculating its intensity distribution; The +1st order object light of the spatial filter is blocked, allowing only the 0th order reference light to illuminate the target surface of the 3CMOS camera. By moving the 3CMOS camera, reference light intensity maps are acquired under focused, overfocus, and underfocus conditions. Following the aforementioned color image decoupling method, monochrome images of focused, overfocus, and underfocus conditions are obtained for different channels. The phase is calculated using the TIE equation, and then the phase information of the R, G, and B channels is obtained. , , The amplitude term, combined with phase information, reconstructs the complex amplitude of the reference light, and obtains the complex amplitude distribution of the reference light under different defocus states.

6. The method as described in claim 5, characterized in that: The method for implementing step three is as follows: Through formula ,in It is the +1st order sidelobe signal obtained in step one. It is the reference optical complex amplitude reconstructed from the TIE obtained in step two. It is the reference light intensity in the focused state. This represents the corrected sidelobe signal; it achieves decoupling of the complex amplitude of the object beam and the reference beam, and obtains the corrected +1 level spectral information under different channels.

7. The method as described in claim 6, characterized in that: Step four is implemented as follows: Using formula The corrected +1-level spectral information is multiplied by the angular spectral transfer function to obtain the corrected object beam angular spectrum for different channels. An inverse Fourier transform is then performed on the corrected angular spectrum to finally obtain the corrected object beam complex amplitude for different channels. , , .

8. The method as described in claim 7, characterized in that: Step five is implemented as follows: The object light complex amplitude at the z=0 plane after R, G, and B channel compensation , , The complex amplitude distribution is transformed to the frequency domain using Fourier transform to obtain the angular spectra corresponding to the three channels. Using the angular spectrum transfer function mentioned in step four, it is propagated to the same spatial reference plane, which is parallel to the initial plane and separated from it by a propagation distance along the optical axis. The propagated angular spectrum is obtained by multiplying the initial plane z=0 angular spectrum by the angular spectrum transfer function of the corresponding channel using the formula. The angular spectra of each channel at the plane are transformed back into the spatial domain to obtain the angular spectra on the same spatial reference plane. The complex amplitude distribution of the three objects on the screen: Red channel object optical complex amplitude; : Green channel optical recovery amplitude; Blue channel object optical complex amplitude; Using formula , The intensity distribution of the three channels on the same spatial plane was obtained. , , Then, the axial differential of light intensity is calculated through chromatic aberration, and the TIE equation is solved to obtain the phase; the phase obtained from the solution. Converted to the actual height of the sample This enables real-time quantitative phase demodulation based on white light diffraction digital holography, i.e., real-time quantitative phase detection.

9. The method as described in claim 8, characterized in that: The two-dimensional window function is a rectangular window or a circular window.

Images