{"id":11242,"date":"2022-11-22T05:18:54","date_gmt":"2022-11-22T05:18:54","guid":{"rendered":"https:\/\/www.szlaser.com\/?page_id=11242"},"modified":"2022-11-22T13:39:06","modified_gmt":"2022-11-22T13:39:06","slug":"optical-design","status":"publish","type":"page","link":"https:\/\/www.szlaser.com\/index.php\/wiki\/optical-design\/","title":{"rendered":"Optical design of THz image surface scanning with an off axis parabolic mirror"},"content":{"rendered":"

Optical design of THz image surface scanning with an off axis\u00a0parabolic mirror<\/h1><\/h1><\/div>

THz; off axis parabolic mirror; image surface scanning; optical design<\/p>\n<\/div>

Abstract<\/h3><\/h3><\/div>

In order to improve the THz imaging speed, an image surface scanning THz fast imaging system was designed. It was a single pixel imaging system basing on the reflection type. The system collected THz by an off axis parabolic mirror which was used to realize the imaging of large caliber, high transmittance, high quality imaging. The optical parameters of system were that F\/# was 2.93, the aperture diameter was 120 mm, the field angle was \u00b11\u00b0, the focus length was 293.45 mm, the size of imaging window was 64 mm\u00d764 mm, the diameter of circular hole was 2 mm, the imaging speed of 16\u00d716 pixels was 0.1 min, the imaging speed of 32\u00d732 pixels was 0.47 min, the imaging speed of 64\u00d764 pixels was 1.7 min, and the spatial resolution was 10 mm. The system combined with compressed sensing theory and image surface scanning theory realized the fast imaging property.<\/p>\n

A rotation plate with holes was inserted at image surface position, which scanned the THz intensity. Then a light cone was employed to collect energy to the Golay detector. The device output image by a special situation of compressed sensing theory that the sample number equaled to the image pixels. Sequentially, the regular least squares algorithm was used to reconstruct intensity distribution. The system has the property of high imaging speed and resolution, low costs, and small structure.<\/p>\n<\/div>

0 Introduction<\/h3><\/h3><\/div>

Terahertz waves are electromagnetic waves with frequencies in the range of 0.1 to 10 THz, which are located in the middle of the infrared band and the microwave band. Terahertz electromagnetic waves, also known as T-rays, fall into the category of far-infrared and submillimeter waves.<\/p>\n

In the past 20 years, terahertz has undergone profound changes, and as new materials provide high-power emission sources, terahertz has been used in more and more research fields. Terahertz signals have strong penetrating power. Terahertz imaging technology is widely used in material detection, non-destructive testing, security scanning and medical fields. Terahertz imaging technology mainly includes time-domain spectral imaging, tomography, and holographic imaging. and continuous wave imaging, etc.<\/p>\n

The time-domain spectral imaging system extracts data reflecting sample information from the time-domain waveform of the electric field for imaging. Time-domain imaging has high working bandwidth and high imaging resolution, but the scanning time is long. Compared with time-domain spectral imaging, continuous terahertz imaging only detects the intensity information of electromagnetic waves after passing through the sample or reflected by the sample, and does not have the ability to provide phase information. information capacity.<\/p>\n

However, the continuous terahertz imaging system has the characteristics of high radiation power, simple system, low price, fast imaging speed, and convenient use. For scanning objects that are relatively large and only need to detect defects or transmission properties, continuous terahertz imaging has obvious advantages.<\/p>\n

The THz imaging technology used before is mainly point-by-point scanning imaging, but point-by-point scanning imaging will reduce the sampling speed. At present, it takes about 20 minutes to obtain an image of 100 \u00d7 100 pixels in the current mechanical point-by-point scanning method. Disadvantages of high degree and high cost.<\/p>\n

Therefore, finding more and better THz imaging methods is also one of the focuses of current THz imaging research. The off-axis parabolic mirror THz imaging technology based on image plane scanning is a new imaging technology developed by applying the compressed sensing theory of signal compression to THz imaging.<\/p>\n

This method can avoid the traditional mechanical point-by-point scanning, abandon the expensive and complex terahertz array detectors, and combine the advantages of high reflectivity and aspheric aberration of off-axis parabolic mirrors to achieve real high-quality fast terahertz. imaging method.<\/p>\n<\/div>

1 Principle<\/h3><\/h3><\/div>

1.1 Scanning principle<\/h3><\/h4><\/div>

The traditional signal acquisition and processing process mainly includes four parts: sampling, compression, transmission and decompression, which must satisfy Shannon’s theorem, that is, the sampling frequency cannot be lower than 2 times of the analog signal frequency. In the traditional signal transmission compression process, the signal is first transformed, and then a small number of coefficients with large absolute values are compressed and encoded, and zero or close to zero coefficients are discarded. This data compression discards most of the previously collected data. Affects the final result or image, but captures a lot of wasteful information that consumes time and resources.<\/p>\n

If the signal itself is compressible, the compressed data of the signal can be directly obtained by using compressed sensing theory, thereby saving time and reducing unnecessary data acquisition process. The core idea is that the compressible signal is sparse in a certain transform domain.<\/p>\n

In this way, the high-dimensional signal obtained from the transformation of the transformation basis and the uncorrelated observation matrix can be projected onto a low-dimensional space, and then the original signal can be obtained by optimizing the solution. This method breaks through the Shannon sampling theorem.<\/p>\n

The measurement process of the compressed sensing theory is linear, assuming that P is a two-dimensional original signal of length N, and the measured value Y is the linear projection of the original signal under the measurement matrix \u03a6. The projection formula is:<\/p>\n

\"\"<\/p>\n

where: M represents the number of measurements, so Y is a two-dimensional signal of length M\u00d7N, When M=N, \u03a6M\u00d7N is a square matrix, and the equation is a well-posed equation, which is easy to solve. Figure 1 shows the calculation process of the 2\u00d72 pixel image according to the above formula.<\/p>\n

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Fig.1 Measurement matrix equation<\/p><\/div>\n<\/div>

1.2 Selection of imaging methods<\/h3><\/h4><\/div>

THz optical systems need to be designed according to the application. At present, the structural forms of optical systems are mainly divided into refraction type, catadioptric type and reflection type. The THz optical system design should meet the following requirements:
\n(1) Small size, easy to install and debug the whole machine;
\n(2) Relative aperture as large as possible;
\n(3) Field of view that meets the requirements;
\n(4) Minimum radiant energy loss in the selected band;
\n(5) Adapt to different environments, and have reliable and stable optical performance, etc.<\/p>\n

Refraction (transmission) THz optical system has the characteristics of large field of view, low F number, mature processing and adjustment technology, various aberrations can be eliminated, light and compact structure, good transmission and stable performance. In the two-dimensional imaging optical system, photoelectric crystals are generally used for detection, and the object distance of the optical system is much larger than the focal length of the lens.<\/p>\n

Its imaging resolution \u0394=1.22\u03bbDt<\/sub> f\/(Ds<\/sub>D); when the size of the detection crystal, the diameter of the lens and the detection wavelength are determined, the harmonic diffraction\/refractive zoom optical system as shown in Fig. 2 can be designed to obtain an image with a certain resolution. However, this design is limited by material properties, and the loss of light energy is relatively large. It is difficult to achieve a design with a large aperture and a long focal length, and it is difficult to increase the relative aperture and the length of the compression structure.<\/p>\n

\"\"

Fig.2 Diagram of THz refraction zoom optical system<\/p><\/div>\n

The off-axis three-reflection THz optical system has the advantages of easy access to large-diameter reflective materials, no chromatic aberration and better correction of spherical aberration and coma aberration, small light energy loss, wide operating band, and short total system length. As shown in Figure 3, Figure 3(a) is a schematic diagram of an off-axis three-mirror optical system; Figure 3(b) is a diagram of a coaxial three-mirror optical system.<\/p>\n

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Fig.3 Diagrams of off-axis three-mirror optical system and on-axis three-mirror anastigmatic system (a)<\/p><\/div>\n

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Fig.3 Diagrams of off-axis three-mirror optical system and on-axis three-mirror anastigmatic system (b)<\/p><\/div><\/p>\n

Using ZEMAX optical imaging design software, the initial structure calculation is realized by writing simple ZPL macros and the diaphragm and field of view are off-axis, and then the ideal optical system is designed through the optimization calculation. However, its F-number is relatively large, the center blocks light, the complexity of the optical-mechanical structure increases, the processing and assembling are difficult, the stray light is not easy to control, and the production cost is high, and it is difficult to meet the requirements of large-field and large-aperture imaging.<\/p>\n

Since materials with good transmission properties in the terahertz band are very scarce at present, lenses suitable for the terahertz band are difficult to obtain, and lenses suitable for terahertz materials are not suitable for visible light, and the system is very difficult to tune.<\/p>\n

Therefore, refracting and catadioptric systems are difficult to achieve in the terahertz band. Due to the complex design of the off-axis three-mirror system, the system F number is low, and it is difficult to assemble and adjust. The off-axis parabolic mirror system is less affected by the material limitation, the reflective material is easier to obtain than the refracting material, the energy attenuation is small, and there is no chromatic aberration at all, and it can be used. Eliminate the influence of spherical aberration, wide applicable band, high system transmittance, convenient for lightweight design.<\/p>\n

However, the currently available off-axis parabolic mirrors are mainly used for collimating terahertz waves, and their apertures are small, so they are not suitable for long-distance imaging. Therefore, ZEMAX optical design software is used to design the optical system of the large-diameter and high-reflectivity off-axis parabolic mirror to ensure the quality of terahertz imaging.<\/p>\n<\/div>

1.3 Imaging principle<\/h3><\/h4><\/div>

The working principle of the imaging device is:
\nThe terahertz wave reflected from the target contained in the observed instantaneous field of view is irradiated by the active terahertz radiation source, and is reflected and imaged on the focal plane by the off-axis parabolic mirror. The metallic light cone collects all the energy focused on the imaging window, sampled with a terahertz single-pixel detector. In this way, the data obtained by the detector is the result data of the inner product of the corresponding pattern of the instantaneous disk on the imaging window and the image intensity of the image plane.<\/p>\n

If the disk rotates at a constant speed according to the set speed, the image surface light and different patterns of the imaging window are multiplied within one cycle of rotation. At the same time, the inner product result of each time is recorded, that is, the inner product data array is obtained.<\/p>\n

The pattern on the imaging window is fixed at each moment when the disk rotates once, that is, the measurement matrix is also fixed. And through the pre-experiment calibration, it can be obtained that the whole measurement process belongs to linear measurement, and finally through the product of the inverse matrix of the measurement matrix and the inner product array, the energy intensity distribution of the image surface is inverted, and the original signal, that is, the target image, is obtained.<\/p>\n

Before using the device, the disk matrix needs to be measured, and the visible light integrating sphere is used to provide uniform light source illumination, so that the radiance or illuminance illuminated on the disk imaging window is almost uniform. Then use the visible light band detector with the same sampling frequency as the GOLAY detector to perform the same frequency sampling and the same frequency and the same initial position rotation to measure the single pixel intensity image within a period of time to save the data.<\/p>\n

Due to the high uniformity of the brightness or illuminance of the image plane, it can be considered that the energy reaching the imaging window is uniform, the measured intensity is normalized, and then the relative measurement method is used to measure the energy intensity value at the position of the imaging window, according to the formula (projection formula in above) can obtain the measurement matrix \u03a6M\u00d7N of the circular hole in the frequency and the test time range. When \u03a6M\u00d7N is determined, the matrix can be used to calculate the energy intensity of the imaging window position in the actual measurement.<\/p>\n

Figure 4 is a schematic diagram of the system image scanning disk designed by CAD. The size of the imaging window is 64 \u00d7 64 mm, the size of the circular hole is 2 mm, and the rotation speed corresponds to the number of pixels of the final output image.<\/p>\n

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Fig.4 Schematic diagram of plate with holes<\/p><\/div>\n<\/div>

2 Device imaging modes<\/h3><\/h3><\/div>

Due to the low terahertz radiation energy in nature, an external active radiation light source is required to perform terahertz active illumination on the target object. The image plane scanning terahertz fast imaging equipment consists of an active radiation illumination system, a reflection imaging system, an image plane scanning system, an energy collection system and a detection system, as shown in Figure 5.<\/p>\n

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Fig.5 System structure<\/p><\/div>\n

The active radiation system consists of a CW continuous terahertz radiation source 1; the reflective imaging system consists of a self-designed gold-coated off-axis parabolic mirror 2; the image plane scanning system is composed of a porous disc 3, a fixed imaging window 4, and a rotary motor 5; the energy collection system is composed of a terahertz high reflectivity metal light cone 6 ; the detection system is composed of a terahertz single-pixel GOLAY detector 7 .<\/p>\n

The CW continuous terahertz radiation source provides tens of milliwatts of high-power radiation to the target object; the gold-coated off-axis parabolic mirror can achieve large-diameter, high-reflectivity, and high-quality imaging. Its clear aperture is 120 mm, and the system at the image plane is designed. The diameter of the diffused spot is much smaller than the diameter of the system Airy disk, and the imaging quality reaches the diffraction limit.<\/p>\n

The image plane scanning system is composed of a fixed imaging window and a rotating porous disk to achieve dynamic scanning at the image plane, so that the pattern of the porous disk in the imaging window and the instantaneous image plane energy intensity at each instant have an inner product effect, and the motor drives the dynamic scanning of the image plane. The disc rotates, and a limited number of sampled intensities and disc patterns are internally integrated within a cycle period. The number of inner products is equal to the number of pixels of the final image to be obtained. When the disc design is completed and the rotation period is determined, then in one cycle The disk pattern matrix displayed on the inner imaging window is a definite value, corresponding to the number of pixels in the result image, a definite measurement matrix \u03a6M \u00d7N is obtained.<\/p>\n

The detection system uses a terahertz GOLAY detector with a typical response time of 25 ms and a sampling frequency of up to 40 Hz. A certain number of samples are collected in one cycle, and the measured data is YM\u00d7N. The principle of image processing is based on the linear measurement relationship YM\u00d7N = \u03a6M\u00d7N PN\u00d7N, the equation system is established by the measurement matrix and the measurement data, and the regularized least squares method is used.<\/p>\n

\"\"<\/p>\n

Fast and accurate solution, get the original signal XN\u00d7N to get the target image, According to the above principle analysis and calculation of sampling time, when the size of the imaging window is 64 \u00d7 64 mm, According to the typical detector sampling frequency of 40 Hz, it can be calculated that: when the number of reconstructed pixels is 256, the sampling time is 0.1 min; when the number of reconstructed pixels is 1024, the sampling time is 0.42 min; when the number of reconstructed pixels is 4 096, the sampling time is 1.7 min.<\/p>\n<\/div>

3 Design Examples<\/h3><\/h3><\/div>

In the design of the optical system, the virtual plane in front of the mirror is used as the global coordinate reference plane. Based on the design of the coaxial reflective optical system, a complete system design is obtained by adding off-axis eccentricity and tilt optimization. First, on the basis of the coaxial system, according to geometric optics and aberration theory, the focal length of the coaxial system is 1\/2 of the radius of curvature of the mirror, that is, f=r\/2, and the initial structure of the optical system including the mirror is calculated. The curvature of the vertex, the conic coefficient, the interval and other parameters, and then set the diameter of the entrance pupil of the system, the radius of curvature of the mirror and the thickness of the interval, the size of the image surface is set to be equal to the width of the imaging window, and the eccentricity of the system is determined by the formula in below calculate:<\/p>\n

\"\"<\/p>\n

where:
\nc is the radius of curvature of the vertex;
\nr is the radial coordinate unit of the lens;
\nk is the aspheric coefficient constant.
\nWhen k<-1, it is a hyperboloid, when k=-1, it is a paraboloid, when -1<k<0, it is an ellipsoid, and when k=0, it is a sphere.<\/p>\n

So take k=-1. Set the initial off-axis eccentricity value of the mirror according to formula above, and set the eccentricity and tilt of the image surface to correspond to the mirror, so as to ensure the imaging quality at the image surface, and then offset the mirror off-axis. The final design result is obtained by setting the threshold of the Merit Function optimization function: the eccentricity DY represents the y-direction eccentricity relative to the reference surface; the inclination angle TX represents the rotation angle relative to the reference surface around the x-axis, clockwise is positive, and counterclockwise is negative; the aspheric coefficient Conic\/4th represents the conic coefficient of the lens surface\/4th degree aspheric coefficient. The optical design diagram of the off-axis parabolic mirror is shown in Figure 6, and the structural parameters of the optical design system are shown in Table 1.<\/p>\n

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Fig.6 Optical design diagram of parabolic mirror<\/p><\/div>\n

Tab.1 Parameter of optical design<\/strong><\/p>\n\n

\n \n \n\n \n \n \n \n\n\n wdt_ID<\/th> Surface<\/th> Radius\/mm<\/th> Interval\/mm<\/th> Offset DY\/mm<\/th> Tilt angle TX\/(\u00b0)<\/th> Material<\/th> Aspheric coefficient<\/th> <\/tr>\n<\/thead>\n \n\n \n \n\n \n \n \n
1<\/td>\n Object surface<\/td>\n \u221e<\/td>\n 20000<\/td>\n 0<\/td>\n 0<\/td>\n Air<\/td>\n 0\/0<\/td>\n <\/tr>\n
2<\/td>\n Mirror<\/td>\n -586.905<\/td>\n -297.780<\/td>\n 200<\/td>\n 0<\/td>\n Mirror<\/td>\n -1<\/td>\n <\/tr>\n
3<\/td>\n Imaging plane<\/td>\n \u221e<\/td>\n 0<\/td>\n -203.344<\/td>\n -37.636<\/td>\n Air<\/td>\n 0<\/td>\n <\/tr>\n <\/tbody> \n\n \n \n \n\n <\/table>\n\n<\/div>