CN113639965A - Spectral resolution acquisition method for single-lens spectrum device - Google Patents

Spectral resolution acquisition method for single-lens spectrum device Download PDF

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CN113639965A
CN113639965A CN202110868969.0A CN202110868969A CN113639965A CN 113639965 A CN113639965 A CN 113639965A CN 202110868969 A CN202110868969 A CN 202110868969A CN 113639965 A CN113639965 A CN 113639965A
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focal
wavelength
lens
spectral resolution
lambda
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CN113639965B (en
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何培栋
袁艳
吕群波
王建威
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Aerospace Information Research Institute of CAS
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Abstract

The invention discloses a spectral resolution acquisition method for a single-lens spectrum device, which comprises the steps of firstly, acquiring an image comprising a quasi-focal image and an out-of-focus image of each wave band by using the single-lens spectrum device; calculating the spectral resolution of the single-lens spectrum device according to the diffraction energy concentration ratio of the in-focus wavelength and the out-of-focus wavelength in one pixel of the acquired image, specifically: the quasi-focal wavelength lambda1Intensity values collected at maximum depth of focus and at off-focus wavelength λ2The condition that the intensity values collected at the focal positions are equal is defined as a critical condition, and the spectral resolution is calculated according to the critical condition. The method can accurately acquire the spectral resolution by aiming at the single-lens spectrum device, has high efficiency and simple calculation process, and overcomes the defect that the single-lens spectrum acquisition device cannot directly utilize Rayleigh criterion to calculate the spectral resolution.

Description

Spectral resolution acquisition method for single-lens spectrum device
Technical Field
The invention relates to the technical field of spectrum instruments, in particular to a spectral resolution acquisition method for a single-lens spectrum device.
Background
At present, for a spectrum instrument, spectral resolution is a very critical index, the spectral resolution refers to the minimum wavelength interval that can be resolved, a common acquisition method for the spectral resolution in the prior art is a rayleigh criterion, and the rayleigh criterion indicates: the separation between two points that can be resolved is equal to the airy disk radius, which also means that the diffraction patterns of two points partially coincide, the center of one diffraction pattern coincides with the first dark ring of the other diffraction pattern, and in the resultant of the light intensity distribution curves of the diffraction patterns of the two points, the maximum value of the light intensity differs from the minimum value by 26%.
However, for the single-lens spectroscopic apparatus, the spectral resolution cannot be calculated by directly using the rayleigh criterion, and there is no spectral resolution acquisition scheme for the single-lens spectroscopic apparatus in the prior art.
Disclosure of Invention
The invention aims to provide a spectral resolution acquisition method for a single-lens spectrum device, which can accurately acquire spectral resolution for the single-lens spectrum device, has high efficiency and simple calculation process, and overcomes the defect that the single-lens spectrum acquisition device cannot directly analyze the spectral resolution by utilizing Rayleigh criterion.
The purpose of the invention is realized by the following technical scheme:
a method of spectral resolution acquisition for a single-lens spectroscopic device, the method comprising:
step 1, firstly, acquiring an image comprising a quasi-focal image and an out-of-focus image of each wave band by using a single-lens spectrum device;
step 2, calculating the spectral resolution of the single-lens spectrum device according to the diffraction energy concentration ratio of the quasi-focal wavelength and the out-of-focus wavelength in one pixel of the acquired image, specifically:
the quasi-focal wavelength lambda1Intensity values collected at maximum depth of focus and at off-focus wavelength λ2The condition that the intensity values collected by the focal positions are equal is defined as a critical condition, and the spectral resolution is calculated according to the critical condition;
wherein d represents the quasi-focal wavelength λ1Depth of focus of (d), f (λ)1) And f (lambda)2) Respectively, the quasi-focal wavelength lambda1And a defocus wavelength lambda2The focal position of (a);
when quasi-focal wavelength lambda1Intensity at maximum depth of focus position and intensity at f (lambda)2) When the intensities of the positions are equal, a critical condition is defined, and the wavelength difference at this time is the spectral resolution δ λ, which is specifically:
δλ＝λ2-λ1。
according to the technical scheme provided by the invention, the method can accurately acquire the spectral resolution aiming at the single-lens spectrum device, has high efficiency and simple calculation process, and overcomes the defect that the single-lens spectrum acquisition device cannot directly utilize Rayleigh criterion to analyze the spectral resolution.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic flowchart of a method for acquiring spectral resolution of a single-lens spectroscopy apparatus according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of spectrum collection according to an embodiment of the present invention;
fig. 3 is a schematic diagram of an acquisition process of the single-lens spectroscopic apparatus according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, not all embodiments, and this does not limit the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flow chart of a method for acquiring spectral resolution of a single-lens spectroscopy apparatus according to an embodiment of the present invention, where the method includes:
step 1, firstly, acquiring an image comprising a quasi-focal image and an out-of-focus image of each wave band by using a single-lens spectrum device;
step 2, calculating the spectral resolution of the single-lens spectrum device according to the diffraction energy concentration ratio of the quasi-focal wavelength and the out-of-focus wavelength in one pixel of the acquired image, specifically:
the quasi-focal wavelength lambda1Intensity values collected at maximum depth of focus and at off-focus wavelength λ2The condition that the intensity values collected by the focal positions are equal is defined as a critical condition, and the spectral resolution is calculated according to the critical condition;
FIG. 2 is a schematic diagram of spectrum collection according to an embodiment of the present invention, and d represents a quasi-focal wavelength λ1Depth of focus of (d), f (λ)1) And f (lambda)2) Respectively, the quasi-focal wavelength lambda1And a defocus wavelength lambda2The focal position of (a);
when quasi-focal wavelength lambda1Intensity at maximum depth of focus position and intensity at f (lambda)2) When the intensities of the positions are equal, a critical condition is defined, and the wavelength difference at this time is the spectral resolution δ λ, which is specifically:
δλ＝λ2-λ1。
in a specific implementation, as shown in fig. 3, a schematic diagram of an acquisition process of the single-lens spectrum device according to the embodiment of the present invention is shown, assuming that a lens diameter of the single-lens spectrum device is 2a, a corresponding focal length is f when a wavelength is λ, and an origin is used as a focal position, and a three-dimensional coordinate system is established;
two dimensionless constants were introduced:
Figure BDA0003188351690000031
wherein z represents the defocus amount on the optical axis; x, y represent the position of the image in a plane perpendicular to the optical axis;
the expression of the intensity of a light beam on the optical axis after passing through a lens is known as follows:
Figure BDA0003188351690000032
the focal length of the lens is expressed as:
Figure BDA0003188351690000033
wherein n represents a lens refractive index; r is1、r2Representing the curvature radius of the lens, and determining the corresponding curvature radius which is a constant after the lens parameters are determined;
the lens refractive index n is different for different wavelengths and is calculated using the Cauchy dispersion formula, which is expressed as:
Figure BDA0003188351690000034
wherein a, b and c represent Cauchy coefficients, which can be obtained by calculation, specifically by fitting according to refractive indexes corresponding to different wavelengths;
from the above equation, the relationship between the focal length f and the wavelength λ is expressed as:
Figure BDA0003188351690000035
in the above formula, R ═ (1/R)1-1/r2) To facilitate presentation;
thereby obtaining the relation between the focal length variation quantity delta f and the wavelength variation quantity delta lambda as follows:
Δf＝f'(λ)Δλ (6)
wherein f' (λ) is determined by the lens parameters, corresponding to the derivative of equation (5), representing the rate of change of focal length with wavelength;
due to the fact that
Figure BDA0003188351690000041
Wherein the content of the first and second substances,
Figure BDA0003188351690000042
wherein u1 and u2 are wavelengths λ respectively1At the position of maximum depth of focus and wavelength lambda2The corresponding u value at the focal position;
bringing formula (8) into formula (7) and simplifying it yields:
Figure BDA0003188351690000043
wherein z is2-z1＝f(λ2)-f(λ1)＝△f；z1And z2Respectively represent the wavelength lambda1And wavelength lambda2A corresponding focal position;
the spectral resolution δ λ is then obtained from equations (9) and (6) as:
Figure BDA0003188351690000044
wherein d represents the quasi-focal wavelength λ1Depth of focus of (d), f (λ)1) And f (lambda)2) Respectively, the quasi-focal wavelength lambda1And a defocus wavelength lambda2The focal position of (a);
the spectral resolution δ λ is derived by combining equation (10) and equation (6) as:
δλ＝△λ＝λ2-λ1。
in addition, the above-mentioned quasi-focal wavelength λ1The focal depth d is approximately equal to 2 Fp;
wherein F ═ F/2a, represents the F number of the system; p represents the pixel size of the detector;
parameters that affect spectral resolution include: F. p and f' (λ);
where F and F' (λ) are both determined by the lens parameters of the single lens spectroscopic assembly and p is determined by the detector chosen.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims. The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.

Claims (3)

1. A method of obtaining spectral resolution for a single-lens spectroscopic apparatus, the method comprising:
step 1, firstly, acquiring an image comprising a quasi-focal image and an out-of-focus image of each wave band by using a single-lens spectrum device;
step 2, calculating the spectral resolution of the single-lens spectrum device according to the diffraction energy concentration ratio of the quasi-focal wavelength and the out-of-focus wavelength in one pixel of the acquired image, specifically:
the quasi-focal wavelength lambda1Intensity values collected at maximum depth of focus and at off-focus wavelength λ2The condition that the intensity values collected by the focal positions are equal is defined as a critical condition, and the spectral resolution is calculated according to the critical condition;
wherein d represents the quasi-focal wavelength λ1Depth of focus of (d), f (λ)1) And f (lambda)2) Respectively, the quasi-focal wavelength lambda1And a defocus wavelength lambda2The focal position of (a);
when quasi-focal wavelength lambda1Intensity at maximum depth of focus position and intensity at f (lambda)2) When the intensities of the positions are equal, a critical condition is defined, and the wavelength difference is the spectral resolutionδ λ, specifically:
δλ＝λ2-λ1。
2. the method for acquiring spectral resolution of a single-lens spectrum device according to claim 1, wherein, in step 2,
assuming that the diameter of a lens of the single-lens spectrum device is 2a, the corresponding focal length is f when the wavelength is lambda, and the origin is taken as the focal position, and establishing a three-dimensional coordinate system;
two dimensionless constants were introduced:
Figure FDA0003188351680000011
wherein z represents the defocus amount on the optical axis; x, y represent the position of the image in a plane perpendicular to the optical axis;
the expression of the intensity of a light beam on the optical axis after passing through a lens is known as follows:
Figure FDA0003188351680000012
the focal length of the lens is expressed as:
Figure FDA0003188351680000013
wherein n represents a lens refractive index; r is1、r2Representing the curvature radius of the lens, and determining the corresponding curvature radius which is a constant after the lens parameters are determined;
the lens refractive index n is different for different wavelengths and is calculated using the Cauchy dispersion formula, which is expressed as:
Figure FDA0003188351680000021
wherein a, b and c represent Cauchy coefficients;
from the above equation, the relationship between the focal length f and the wavelength λ is expressed as:
Figure FDA0003188351680000022
in the above formula, R ═ (1/R)1-1/r2) To facilitate presentation;
thereby obtaining the relation between the focal length variation quantity delta f and the wavelength variation quantity delta lambda as follows:
Δf＝f'(λ)Δλ (6)
wherein f' (λ) is determined by the lens parameters, corresponding to the derivative of equation (5), representing the rate of change of focal length with wavelength;
due to the fact that
Figure FDA0003188351680000023
Wherein the content of the first and second substances,
Figure FDA0003188351680000024
wherein u1 and u2 are wavelengths λ respectively1At the position of maximum depth of focus and wavelength lambda2The corresponding u value at the focal position;
bringing formula (8) into formula (7) and simplifying it yields:
Figure FDA0003188351680000025
wherein z is2-z1＝f(λ2)-f(λ1)＝△f；z1And z2Respectively represent the wavelength lambda1And wavelength lambda2A corresponding focal position;
the spectral resolution δ λ is then obtained from equations (9) and (6) as:
Figure FDA0003188351680000031
wherein d represents the quasi-focal wavelength λ1The depth of focus of; f (lambda)1) And f (lambda)2) Respectively, the quasi-focal wavelength lambda1And a defocus wavelength lambda2The focal position of (a);
the spectral resolution δ λ is derived by combining equation (10) and equation (6) as:
δλ＝△λ＝λ2-λ1。
3. the method for obtaining spectral resolution for a single-lens spectroscopic apparatus according to claim 2,
quasi-focal wavelength lambda1The focal depth d is approximately equal to 2 Fp;
wherein F ═ F/2a, represents the F number of the system; p represents the pixel size of the detector;
parameters that affect spectral resolution include: F. p and f' (λ);
where F and F' (λ) are both determined by the lens parameters of the single lens spectroscopic assembly and p is determined by the detector chosen.
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