CN114046731B - Submicron single photon magnitude tiny light spot measuring method based on silicon photomultiplier - Google Patents

Submicron single photon magnitude tiny light spot measuring method based on silicon photomultiplier Download PDF

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CN114046731B
CN114046731B CN202111279574.3A CN202111279574A CN114046731B CN 114046731 B CN114046731 B CN 114046731B CN 202111279574 A CN202111279574 A CN 202111279574A CN 114046731 B CN114046731 B CN 114046731B
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silicon photomultiplier
light
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pulse
displacement table
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CN114046731A (en
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张国青
杨亚贤
曹馨悦
张晨
刘丽娜
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Xi'an Minwei Electric Power Technology Co ltd
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Xian Polytechnic University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01JMEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J1/00Photometry, e.g. photographic exposure meter
    • G01J1/42Photometry, e.g. photographic exposure meter using electric radiation detectors
    • G01J1/44Electric circuits
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01JMEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J1/00Photometry, e.g. photographic exposure meter
    • G01J1/42Photometry, e.g. photographic exposure meter using electric radiation detectors
    • G01J1/44Electric circuits
    • G01J2001/4446Type of detector
    • G01J2001/4453PMT

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Abstract

The invention discloses a submicron single-photon-magnitude tiny light spot measuring method based on a silicon photomultiplier, which utilizes the silicon photomultiplier as a single-photon response detector, combines a precise displacement table, and obtains the size and the spatial distribution of light intensity of a single-photon-magnitude pulse laser light spot focused by a microscope objective through two-dimensional or one-dimensional spatial scanning and deconvolution operation.

Description

Submicron single photon order tiny light spot measuring method based on silicon photomultiplier
Technical Field
The invention belongs to the technical field of optical measurement and semiconductor optoelectronics, and particularly relates to a submicron single-photon-level micro-light spot measurement method based on a silicon photomultiplier.
Background
The micro-spot focusing technology has important application in a plurality of fields. Such as laser auto-collimation and measurement, optical information storage and transmission, biological micro-fluidic tube preparation, etc., require focusing of the spot to a very small size. The single-photon-level micro light spot has important application in the fields of single-photon imaging, time-dependent fluorescence lifetime spectroscopy, optical quantum information processing and the like. At present, common measurement methods for micro light spots include: flat panel/planar detector measurement, (slit, knife edge, pinhole) scanning methods, CCD (charge coupled device) methods, etc. Jain a et al (a.jain, a.panse, d.r.bednarek, s.rudin, focal spot measurement using a digital Flat panel detector, spie Medical Imaging,9033 (90335F) (2014)) use a 194 μm pixel Flat Panel Detector (FPD) in conjunction with a micro-pinhole (10 μm) to measure the Focal spot using a deconvolution method to reduce the blurring effect caused by the detector during the measurement of the focused spot, with a measured spot size around 0.6 mm. Takeuchi A et al (A. Takeuchi, Y. Suzuki, K. Uesugi, differential-phase-contrast-edge scan method for precision evaluation of X-ray nanobeams, japan Journal of Applied Physics 54 (9) (2015) 092401.) improved on a knife edge method for micro spots by scanning a focused micro beam with a hard X-ray microbeam knife edge scanning system with a CMOS sensor/CCD using a tantalum thin film knife edge and measuring the focused spot size at 25nm. But this method cannot respond to single photon magnitude pulsed spots. S K Tiwari et al (s.k. Tiwari, s.p. Ram, j. Jayabalan, s.r. Mishra, measuring a narrow Bessel beam spot by scanning a charged-coupled device (CCD) pixel, measuring Science and Technology 21 (2) (2010) 025308.) place the CCD photosurface perpendicular to the beam axis, record the two-dimensional distribution of beam intensity in the scan plane by means of CCD imaging, and measure a 4 μm spot that is similar to and smaller than the pixel size. The CCD used by the method has no single-photon response capability, and cannot realize the pulse light spot measurement of single-photon magnitude. At present, the measurement of the spot size of single photon magnitude is rarely reported. Liuyu et al (liuyu, zhao bin) applied optics, 06 (2007): 680-683.) measured the beam waist spot of 6 μm bessel beams using a photomultiplier tube (PMT) as a light signal detector, but this method uses a PMT that is a vacuum device with a minimum size on the order of centimeters, limiting the integration of the system, and having poor photon number resolution.
Disclosure of Invention
The invention aims to provide a submicron single-photon-level micro light spot measuring method based on a silicon photomultiplier, and solves the problem that pulse light spot measurement of single-photon level cannot be realized in the prior art.
The technical scheme adopted by the invention is as follows: the measuring method of submicron single photon magnitude tiny light spot based on silicon photomultiplier comprises a nanometer displacement table for placing the silicon photomultiplier, wherein the nanometer displacement table is electrically connected with a nanometer displacement table driver and a computer in sequence; a microscope objective with a light path right facing the silicon photomultiplier is arranged below the nano displacement table, a pinhole light-transmitting sheet and an inclined laser beam splitter are sequentially arranged below the microscope objective along the light path direction, a laser head is arranged on one side of the laser beam splitter along the light path direction, and the laser head is electrically connected with a picosecond pulse laser driver; the device also comprises a stabilized voltage power supply and a high-speed low-noise amplifier which are both connected with the silicon photomultiplier, wherein the other end of the high-speed low-noise amplifier is connected with a digital oscilloscope, and the other end of the digital oscilloscope is connected to a computer; the measuring method specifically comprises the following steps:
step 1, placing a silicon photomultiplier in an electromagnetic shielding box, and placing a photosensitive surface of the silicon photomultiplier on a nanometer displacement table in a downward manner;
step 2, horizontally placing a pinhole light-transmitting sheet with a central hole on a light path between the laser beam splitter and the microscope objective;
step 3, enabling the laser head to irradiate a picosecond laser beam by a picosecond pulse laser driver, splitting the picosecond laser beam by a laser beam splitter, and enabling the picosecond laser beam to be focused into light spots on the surface of the silicon photomultiplier through a microscope objective;
step 4, supplying power to the silicon photomultiplier through a voltage-stabilized power supply to enable the silicon photomultiplier to reach a Geiger avalanche mode, amplifying an output avalanche pulse signal through a high-speed low-noise amplifier, and inputting the amplified avalanche pulse signal into a digital oscilloscope to obtain a pulse counting rate;
step 5, controlling a driver of the nanometer displacement table by using a program of a computer to move the nanometer displacement table, and acquiring pulse counting rate distribution at different positions;
and 6, performing deconvolution operation on the pulse counting rate distribution at different positions acquired by the computer and the shape function of an avalanche diode unit in the silicon photomultiplier, and fitting a Bessel function on the deconvolution operation result to obtain spot size information.
The present invention is also characterized in that,
and 2, forming a pinhole with the aperture not more than 100 micrometers in the center of the pinhole light-transmitting sheet in the step 2.
And 3, adjusting the intensity of the picosecond laser beam through a picosecond pulse laser driver to ensure that the counting rate of the silicon photomultiplier avalanche is lower than 10% of the repetition frequency of the picosecond laser beam.
The repetition rate of the picosecond laser beam is 1-100 MHz.
In step 6, a spatial distribution function f (x, y) of the relative light intensity of the focused laser spot is obtained by performing deconvolution operation, and is expressed by a formula (1):
f(x,y)=F -1 {F(f x ,f y )} (1)
in the formula (1), x, y are coordinates in a beam waist section perpendicular to a beam propagation direction, F -1 {F(f x ,f y ) Is the inverse Fourier transform of F (x, y), F (F) x ,f y ) Is a fourier transform form of f (x, y) and is represented by equation (2):
F(f x ,f y )=H(f x ,f y )/G(f x ,f y ) (2)
in the formula (2), H (f) x ,f y )、G(f x ,f y ) Expressed sequentially by equations (3), (4) as:
Figure BDA0003328203000000041
Figure BDA0003328203000000042
in the formulae (3) and (4), L 0 For the spatial extent of the scan, H (f) x ,f y ) In the form of a Fourier transform of the pulse count rate distribution function h (x, y), G (f) x ,f y ) In the form of a fourier transform of the shape function g (x, y) of the avalanche diode cell, i is in imaginary units and e is a natural base.
The beneficial effects of the invention are:
(1) The method can measure the micro light spots of the single photon submicron order;
(2) The light spot and the detector are easy to align without precise adjustment and without an optical slit/knife edge or a pinhole, and the size of the light spot to be detected and the spatial distribution information of the light intensity can be obtained by utilizing a tiny APD unit array in the SiPM through fast moving scanning and deconvolution operation;
(3) The method has practical value in the field of tiny weak light spot detection and related application thereof.
Drawings
FIG. 1 is a schematic diagram of a device based on a submicron single photon magnitude micro light spot measurement method based on a silicon photomultiplier according to the present invention;
FIG. 2 is a schematic flow chart of a measuring method of submicron single photon-level micro light spots based on a silicon photomultiplier according to the present invention;
fig. 3 a) is a diagram of the present invention using FBK SiPM (model: LF-HD) measured pulse count rate one-dimensional distribution map;
fig. 3 b) is a graph of the present invention using NDL SiPM (model: EQR 1011-1010C-T) measured pulse count rate two-dimensional distribution graph;
fig. 3 c) is a graph of the present invention using Hamamatsu SiPM with a cell size of 10 μm (model: S12571-010C) measuring the pulse counting rate one-dimensional distribution graph;
fig. 3 d) is a block diagram of the present invention using FBK SiPM with a cell size of 35 μm (model: LF-HD) measured pulse count rate two-dimensional distribution graph;
fig. 3 e) is a graph of the present invention using NDL SiPM (model: EQR 1011-1010C-T) measured pulse count rate two-dimensional distribution graph;
fig. 3 f) the invention uses a Hamamatsu SiPM with a cell size of 10 μm (model: S12571-010C) measuring a pulse counting rate two-dimensional distribution graph;
fig. 4 a) is a block diagram based on the invention using FBK SiPM with a cell size of 35 μm (model: LF-HD) and a Bessel fitting graph;
FIG. 4 b) is a graph of one-dimensional deconvolution results and Bessel fits based on the present invention using NDL SiPM (EQR 1011-1010C-T) with cell size of 10 μm;
fig. 4 c) is a graph based on the invention using Hamamatsu SiPM with a cell size of 10 μm (model: S12571-010C) and a Bessel fitting chart.
In the figure, 1, a regulated power supply, 2, a high-speed low-noise amplifier, 3, a digital oscilloscope, 4, a nanometer displacement table driver, 5, a nanometer displacement table, 6, a picosecond pulse laser driver, 7, a laser head, 8, a laser beam splitter, 9, a pinhole light-transmitting sheet, 10, a microscope objective, 11, a silicon photomultiplier and 12, a computer.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention provides a submicron single photon magnitude tiny light spot measuring method based on a silicon photomultiplier, and the device based on the method is shown in figure 1 and comprises a nanometer displacement table 5 for placing a silicon photomultiplier 11, wherein the nanometer displacement table 5 is sequentially and electrically connected with a nanometer displacement table driver 4 and a computer 12; a microscope objective 10 with a light path right opposite to the silicon photomultiplier 11 is arranged below the nanometer displacement table 5, a pinhole light-transmitting sheet 9 and an inclined laser beam splitter 8 are respectively arranged below the microscope objective 10 along the light path direction, a 375 nanometer laser head 7 is arranged on one side of the laser beam splitter 8 along the light path direction, and the laser head 7 is electrically connected with a picosecond pulse laser driver 6; the device also comprises a stabilized voltage power supply 1 and a high-speed low-noise amplifier 2 which are both connected with the silicon photomultiplier 11, the other end of the high-speed low-noise amplifier 2 is connected with a digital oscilloscope 3, and the other end of the digital oscilloscope 3 is connected with a computer 12; the measuring method specifically comprises the following steps as shown in fig. 2:
step 1, placing a silicon photomultiplier 11 in an electromagnetic shielding box, and arranging a piezoelectric ceramic (PZT) nano displacement table 5 with a photosensitive surface facing downwards to control the position of the silicon photomultiplier 11; the silicon photomultiplier tube 11 is composed of a tiny array of Avalanche Photo Diode (APD) cells, gaps are formed among the APD cells, square APDs correspond to square wave functions or are called as rectangular functions, the photosensitive area of the silicon photomultiplier tube 11 is over millimeter square and is far larger than a single photon avalanche photo diode (SPAD), therefore, alignment of light spots and a detector is easy to achieve, and an optical slit/knife edge or a pinhole is not needed in front of the detector.
The model of the silicon photomultiplier 11 used for the measurement was selected from FBK SiPM (LF-HD, italy), NDL SiPM (EQR 1011-1010C-T, china), and Hamamatsu SiPM (S12571-010C, manufactured by Nippon Kogyo Co., ltd.), and the cell sizes were 35X 35 μm 2 (FBK)、10×10μm 2 (NDL)、10×10μm 2 (Hamamatsu); the piezoelectric ceramic (PZT) nanometer displacement table is Pinano XYZ (closed loop displacement precision 2nm; displacement range 200 μm, germany)
Step 2, horizontally placing a pinhole light-transmitting sheet 9 with a central hole on an optical path between the laser beam splitter 8 and the silicon photomultiplier 11, wherein the center of the pinhole light-transmitting sheet 9 is provided with a pinhole with the aperture of 100 mu m for reducing the diameter of a light spot;
step 3, enabling a laser head 7 to emit picosecond pulse laser beams by a picosecond pulse laser driver 6, and enabling the picosecond pulse laser beams to be focused on the surface of a silicon photomultiplier 11 through a pinhole light-transmitting sheet 9 and a microscope objective 10 after being split by a laser beam splitter 8; the specific treatment method comprises the following steps:
the picosecond pulse laser driver 6 adjusts the intensity of laser generated by the laser head 7, so that the counting rate of the silicon photomultiplier 11 avalanche is lower than 10% of the repetition frequency of the picosecond pulse laser driver 6, and the number of pulse photons reaching the SiPM photosensitive surface is ensured to be attenuated to a single photon level.
Wherein the microscope (including microscope objective lens 10, pinhole light-transmitting plate 9, laser beam splitter 8) is X-73, olympus Corp (objective lens resolution nominal value 0.42 μm, manufactured by Olympus corporation, japan); the picosecond laser beam was PDL-800D375 (center wavelength, 375nm; full width at half maximum, 44ps; repetition frequency, 31.125kHz-80MHz; maximum average light energy, 0.7mW; manufactured by PicoQuant, germany).
Step 4, supplying power to the silicon photomultiplier 11 through the programmable stabilized voltage supply 1 to enable the silicon photomultiplier to reach a Geiger avalanche mode, amplifying the output avalanche pulse signal through the high-speed low-noise amplifier 2, inputting the amplified avalanche pulse signal into the digital oscilloscope 3 to observe the avalanche pulse waveform, and acquiring the pulse counting rate;
the regulated power supply 1 is an IT6235 precision regulated power supply (made in China) and is used for supplying power.
Step 5, controlling a displacement table driver 4 by using an LABVIEW program in a computer 12 to move a nanometer displacement table 5, respectively setting an equivalent photon number threshold value of a digital oscilloscope 3 to be 0.5p.e., displaying and recording a pulse counting frequency of a triggered avalanche pulse signal by the digital oscilloscope 3, collecting the pulse counting frequency by the computer 12, and outputting the pulse counting frequency, namely, one-dimensional and two-dimensional spatial distribution of relative light responsivity on the computer 12;
and step 6, carrying out deconvolution operation on the one-dimensional space distribution of the pulse counting rate acquired by the computer 12 at an LABVIEW program end by using a deconvolution module and a shape function (rectangular function) of an APD unit, importing a deconvolution result into general mathematical software embedded in the computer 12, and fitting by using a Bessel function to obtain light spot size information.
In the experiments of different models of silicon photomultiplier tubes 11 at different times in step 3 and step 4, the distance of SiPM relative to the objective lens needs to be adjusted, and the peak-to-valley ratio is performed by measuring and screening the pulse counting rate one-dimensional spatial distribution for multiple times to ensure that the light spots are at the optimal focusing positions.
The principle of the submicron single photon-level tiny light spot measuring method based on the silicon photomultiplier is as follows:
laser generated by a picosecond pulse laser driver 6 and a laser head 7 is irradiated on a silicon photomultiplier 11 fixed on a nanometer displacement table 5 through a laser beam splitter 8 and a pinhole light-transmitting sheet 9, meanwhile, a stabilized voltage power supply 1 supplies power to the silicon photomultiplier 11, an output avalanche pulse signal is subjected to signal amplification through a high-speed low-noise amplifier 2, waveform and spatial distribution of relative photoresponse of a detector are observed through a digital oscilloscope, a computer 12 collects one-dimensional and two-dimensional spatial distribution of relative photon responsivity generated by avalanche, and a deconvolution module and a rectangular function are used at an LABVIEW program end for deconvolution operation. The operation principle is as follows:
the relative spatial responsivity distribution data h (x, y), the rectangular function g (x, y), and the spot light intensity spatial distribution function f (x, y) relationship can be given by equation (1):
f(x,y)*g(x,y)+ε(x,y)=h(x,y) (1)
in the formula (1), x and y are coordinates in a beam waist section perpendicular to the beam propagation direction, epsilon is noise fluctuation of a measuring signal, the noise fluctuation can be eliminated through a low-pass filtering operation, and an intensity distribution function f (x, y) is obtained through a deconvolution operation. Fourier transform of h (x, y) and g (x, y) is given by the equations (2) and (3):
Figure BDA0003328203000000081
Figure BDA0003328203000000082
l in the formulae (2) and (3) 0 Is the spatial extent of the scan.
F(f x ,f y )=H(f x ,f y )/G(f x ,f y ) (4)
Wherein F (F) x ,f y ) Is a fourier transform version of f (x, y). And then obtaining a spatial distribution function f (x, y) of the focused laser spot relative to the light intensity through inverse Fourier transform:
f(x,y)=F -1 {F(f x ,f y )} (5)
finally, general mathematical software embedded in the computer 12 is used for carrying out Bessel function fitting on the deconvolution result of the light spot, and drawing a one-dimensional distribution diagram of the light spot by using drawing software.
Examples
As shown in FIG. 1, the model of the silicon photomultiplier 11 used in the present embodiment is selected from FBK (LF-HD, italy), NDL (EQR 1011-1010C-T, china) Hamamatsu S12571-010C (Japan); the nano-displacement table 5 is nanoXYZ (no-load resolution 2nm; displacement range, 200 microns, produced by Germany); a microscope (including a microscope objective lens 10 (model HAS-Y-2-40, bandwidth 10kHz-1.9GHz, noise factor 4.9dB, voltage gain 40dB (100 ×), germany), a pinhole light transmitting sheet 9, a laser beam splitter 8) is X-73, olympus Corp., (olympus Corp.); the picosecond pulse laser is PDL-800D375 (center wavelength, 375nm; full width at half maximum, 44ps; repetition frequency, 31.125kHz-80MHz; maximum average light energy, 0.7mW; produced by Germany); the digital oscilloscope 4 is a digital fluorescence oscilloscope DPO4102B-L (sampling rate 5GSa/s,1GHz bandwidth, manufactured by Tektronix corporation of America);
the working principle of the embodiment is as follows:
the silicon photomultiplier 11 detector is fixed on the nanometer displacement table 5, and the silicon photomultiplier 11 can move along the nanometer displacement table 5 in X and Y directions according to a certain step length. The programmable stabilized voltage supply 1 is used for biasing the silicon photomultiplier tube 11 to achieve a Geiger avalanche breakdown state, an avalanche signal generated by avalanche breakdown of the silicon photomultiplier tube 11 is amplified by the high-speed low-noise amplifier 2 and then is introduced into the high-speed digital oscilloscope 3, and the count rate of avalanche pulses at 0.5p.e is obtained. Setting a proper step length at a PC end, moving a silicon photomultiplier 11 fixed on a nanometer displacement table 2 point by point along the X/Y direction, simultaneously measuring and recording the pulse counting rate displayed by a digital oscilloscope 3 on each position point to obtain 0.5p.e. Fig. 3 a) to 3 f) are graphs of one-dimensional pulse count rate and two-dimensional pulse count rate profiles of silicon photomultipliers 11 of different sizes, as can be seen from fig. 3 d) to 3 f): the APD cells are spatially distributed with respect to the optical response, and the different APD cells can be clearly distinguished. From 3 d) the Gap (spacing) region size between APD cells of FBK 35 μm SiPM is 5 μm, so it can be concluded that the spot size (FWHM) is significantly less than 5 μm, given a spot size greater than 5 μm, different APD cells will not be resolvable. FIG. 3 e) is a relative photoresponse spatial one-dimensional/two-dimensional distribution plot of NDL10 μm SiPM, where the APD cells have a period of 10 μm, a photosensitive region size of 7 μm, a Gap size of 3 μm, and yet still be resolved between APDs, indicating that the spot size is less than 3 μm. Details inside the APD cell in 10 μm Hamamatsu SiPM from fig. 3 f) can still be resolved, indicating that the FWHM of the spot size should be less than 1 μm. By deconvolving the square wave with the matrix of fig. 3 a) to 3 c), and fig. 4 a) to 4 c) with a bezier fit, the resulting spot size is about 0.66 μm.

Claims (4)

1. The submicron single photon magnitude tiny light spot measuring method based on the silicon photomultiplier is characterized in that a device based on the measuring method comprises a nanometer displacement table (5) for placing a silicon photomultiplier (11), wherein the nanometer displacement table (5) is sequentially and electrically connected with a nanometer displacement table driver (4) and a computer (12); a microscope objective (10) with a light path right facing a silicon photomultiplier (11) is arranged below the nanometer displacement table (5), a pinhole light-transmitting sheet (9) and an inclined laser beam splitter (8) are sequentially arranged below the microscope objective (10) along the light path direction, a laser head (7) is arranged on one side of the laser beam splitter (8) along the light path direction, and the laser head (7) is electrically connected with a picosecond pulse laser driver (6); the device is characterized by also comprising a stabilized voltage power supply (1) and a high-speed low-noise amplifier (2) which are both connected with the silicon photomultiplier (11), wherein the other end of the high-speed low-noise amplifier (2) is connected with a digital oscilloscope (3), and the other end of the digital oscilloscope (3) is connected to a computer (12); the measuring method specifically comprises the following steps:
step 1, placing a silicon photomultiplier (11) in an electromagnetic shielding box, and placing the silicon photomultiplier on a nanometer displacement table (5) with a photosensitive surface facing downwards;
step 2, horizontally placing a pinhole light-transmitting sheet (9) with a central hole on a light path between a laser beam splitter (8) and a microscope objective (10);
step 3, enabling a laser head (7) to irradiate picosecond laser beams by a picosecond pulse laser driver (6), splitting the picosecond laser beams by a laser beam splitter (8), and enabling the picosecond laser beams to be focused into light spots on the surface of a silicon photomultiplier (11) through a microscope objective (10);
step 4, supplying power to the silicon photomultiplier (11) through a voltage-stabilized power supply (1) to enable the silicon photomultiplier to reach a Geiger avalanche mode, amplifying an output avalanche pulse signal through a high-speed low-noise amplifier (2), and inputting the avalanche pulse signal into a digital oscilloscope (3) to obtain a pulse counting rate;
step 5, controlling a driver (4) of the nano displacement table by using a program of a computer (12) to move the nano displacement table (5) and acquiring pulse counting rate distribution at different positions;
step 6, performing deconvolution operation by using pulse counting rate distribution at different positions acquired by the computer (12) and a shape function of an avalanche diode unit in the silicon photomultiplier (11), and performing Bessel function fitting on a deconvolution operation result to obtain light spot size information; the spatial distribution function f (x, y) of the relative light intensity of the focused laser spot is obtained by deconvolution operation, and is expressed by a formula (1):
f(x,y)=F -1 {F(f x ,f y )} (1)
in the formula (1), x and y are beam waist sections perpendicular to the beam propagation directionIn-plane coordinates, F -1 {F(f x ,f y ) Is the inverse Fourier transform of F (x, y), F (F) x ,f y ) Is a fourier transform form of f (x, y) and is represented by equation (2) as:
F(f x ,f y )=H(f x ,f y )/G(f x ,f y ) (2)
in the formula (2), H (f) x ,f y )、G(f x ,f y ) Expressed sequentially by equations (3), (4) as:
Figure FDA0004050864430000021
Figure FDA0004050864430000022
in the formulae (3) and (4), L 0 For the spatial extent of the scan, H (f) x ,f y ) In the form of a Fourier transform of the pulse count rate distribution function h (x, y), G (f) x ,f y ) In the form of a fourier transform of the shape function g (x, y) of the avalanche diode cell, i is in imaginary units and e is a natural base.
2. The method for measuring the submicron single photon magnitude micro light spot based on the silicon photomultiplier as claimed in claim 1, wherein a pinhole having a pore size not more than 100 μm is formed in the center of the pinhole light-transmitting sheet (9) in the step 2.
3. The method for measuring the submicron single photon magnitude micro light spot based on the silicon photomultiplier as claimed in claim 1, wherein the step 3 adjusts the intensity of the picosecond laser beam through the picosecond pulse laser driver (6) to make the avalanche count rate of the silicon photomultiplier (11) less than 10% of the repetition rate of the picosecond laser beam.
4. The silicon photomultiplier-based submicron single photon magnitude micro spot measurement method according to claim 3, wherein the repetition frequency of the picosecond laser beam is 1-100 megahertz.
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