CN108363202A - A kind of Varied clearance Fabry-Perot interferometer reflectivity determines method - Google Patents
A kind of Varied clearance Fabry-Perot interferometer reflectivity determines method Download PDFInfo
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- CN108363202A CN108363202A CN201810155553.2A CN201810155553A CN108363202A CN 108363202 A CN108363202 A CN 108363202A CN 201810155553 A CN201810155553 A CN 201810155553A CN 108363202 A CN108363202 A CN 108363202A
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Abstract
The invention discloses a kind of Varied clearance Fabry Perot (F P) interferometer reflection rates to determine method, belongs to light spectrum image-forming field.Comprehensive analysis of the present invention influence of Varied clearance Fabry Perot (F P) the interferometer interference cavity reflectivity to Varied clearance Fabry Perot (F P) monochromatic light interference fringe sine and modulation degree that interference spectrum imaging system finally obtains.By using technical scheme of the present invention, sine and modulation degree to interference fringe carry out compromise processing, it can not only determine Varied clearance Fabry Perot (F P) interferometer interference cavity optimum reflectivity value, it can also avoid, because one of performance parameter is excessively poor, Varied clearance Fabry Perot (F P) interference spectrum imaging system being caused to can not work normally.
Description
Technical field
The invention belongs to light spectrum image-forming fields, relate generally to a kind of Varied clearance Fabry-Perot (F-P) interference spectrum imaging
The determination method of Varied clearance F-P interferometer reflection rates in system.
Background technology
As the core devices of Varied clearance Fabry-Perot (F-P) interference spectrum imaging system, Varied clearance F-P interferometers
With its compact structure, compact, the advantages that operation principle simple possible, makes entire interference spectrum imaging system, especially in long wave
Infrared band really meets the demand of lightweight, miniaturization, has widened the application platform of interference spectrum imaging system.Wherein
Varied clearance F-P interferometer interference cavity reflectivity sizes directly affect interference spectrum imaging system and are finally obtaining interference fringe just
String and modulation degree.Interference fringe sine is poor, and secondary lobe is will produce after corresponding Fourier transformation, not only reduces dominant frequency in this way
The intensity of signal, but also some interference signals are will produce, reduce the signal-to-noise ratio of system；Interference fringe modulation degree is poor, and signal becomes
Change amount is small, is unfavorable for the demodulation process of follow-up spectral signal in this way.
The paper that foreign periodical SPIE Vol.8390 are delivered《A compact LWIR hyperspectral
system employing a microbolometer array and a variable gap Fabry-Perot
interferometer employed as a Fourier transform spectrometer》In to describe interferometer dry
The determination method of cavity reflection rate is related to, although this method proposition needs to consider interferometer interference cavity reflectance value to interference fringe just
The influence of string and modulation degree, but both do not provide the specific functional relation between interferometer reflection rate value and obtain two
The method of person and the specific functional relation of interferometer reflection rate value, therefore this article can not be utilized to realize and pass through interference fringe sine
And modulation degree definitely obtains interferometer interference cavity optimum reflectivity value.
Chinese periodical《Acta Optica》The paper that the 8th phase of volume 35 delivers《Bloom based on symmetric wedge interference cavity
Spectrum imaging method》In describe the side that a kind of modulation degree by polychromatic light interference fringe limits interferometer interference cavity reflectivity
The major defect of method, this method is：First, this method only considers the modulation degree of interference fringe, is not considering interference fringe just
String causes to limit obtained interferometer interference cavity reflectivity not being optimal；Secondly, the wavelength band that this method uses is secondary color
Light, the modulation degree and the interferometer angle of wedge and interferometer interference cavity reflectivity of the interference fringe caused are related, and this article
In, the relationship situation of interference fringe modulation degree and interferometer interference cavity reflectivity in the case where only providing certain given interferometer angles of wedge
Under, i.e. the optimal interferometer interference cavity reflectivity of subjective determination is theoretically unsound.
Invention content
The problem of for proposed in above-mentioned background technology, the present invention propose a kind of Varied clearance Fabry-Perot interferometer
Reflectivity determines method, main to realize following three purposes：
1, the monochromatic light interference fringe that one Varied clearance Fabry-Perot (F-P) interference spectrum imaging system obtains is provided
The mathematical model of relationship between sine and Varied clearance Fabry-Perot (F-P) interferometer interference cavity reflectivity.
2, the monochromatic light interference fringe that one Varied clearance Fabry-Perot (F-P) interference spectrum imaging system obtains is provided
The mathematical model of relationship between modulation degree and Varied clearance Fabry-Perot (F-P) interferometer interference cavity reflectivity.
3, provide a Varied clearance Fabry-Perot interference spectrum imaging system obtain monochromatic light interference fringe performance with
Object function between its sine and modulation degree.
To achieve the above object, the technical scheme is that：
A kind of Varied clearance Fabry-Perot interferometer reflectivity determines method, it is characterised in that：Including following step
Suddenly：
Step 1：Establish the monochromatic light interference fringe sine of Varied clearance Fabry-Perot interference spectrum imaging system acquisition
The mathematical model of relationship between Varied clearance Fabry-Perot interferometer interference cavity reflectivity；
Step 2：Establish the monochromatic light interference fringe modulation degree of Varied clearance Fabry-Perot interference spectrum imaging system acquisition
The mathematical model of relationship between Varied clearance Fabry-Perot interferometer interference cavity reflectivity；
Step 3：Mathematical model is obtained according to step 1 and step 2, with multiplying for monochromatic light interference fringe sine and modulation degree
Product is object function, and when target function value maximum, corresponding Varied clearance Fabry-Perot interferometer interference cavity reflectance value is
Optimum reflectivity value.
Further preferred embodiment, a kind of Varied clearance Fabry-Perot interferometer reflectivity determine method, feature
It is：In step 1, the monochromatic light interference fringe sine of Varied clearance Fabry-Perot interference spectrum imaging system acquisition is established
The process of the mathematical model of relationship is between Varied clearance Fabry-Perot interferometer interference cavity reflectivity：
Step 1.1：Establish the monochromatic light relative interference light intensity of Varied clearance Fabry-Perot interference spectrum imaging system acquisition
The mathematical model changed with phase difference：
Wherein Ii(λ) is the corresponding light intensity of incident light of monochromatic light that wavelength is λ, and I (λ) is Varied clearance Fabry-Perot Luo Gan
The monochromatic light relative interference light intensity of spectrum imaging system acquisition is related to, R is interference cavity reflectivity,For the phase between two interference lights
Difference：
X is distance of the horizontal direction interferometer away from optical axis, and α is the interferometer angle of wedge；
In [0,1] interval range, several interference cavity reflectivity values are set, by each interference cavity reflectivity values generation
Enter the mathematical model in this step, each interference cavity reflectivity corresponds to obtain a monochromatic light relative interference light intensity with phase difference variable
The curve of change；
Step 1.2：For each interference cavity reflectivity, a corresponding monochromatic light standard sine function curve is established：Its
The minimum and maximum amplitude of Plays the tracks of line voltage takes the corresponding list of interference cavity reflectivity obtained in step 1.1 respectively
The maximum value and minimum value of coloured light relative interference light intensity amplitude range, the phase difference constant interval of standard sine function curve and take
Value is identical as the calculated value in step 1.1；
Step 1.3：For each interference cavity reflectivity, the monochromatic light relative interference light intensity that calculating step 1.1 obtains is with phase
The relative error for the monochromatic light standard sine function curve that potential difference change curve is obtained with step 1.2 is with phase difference change curve；
Step 1.4：For the corresponding relative error of each interference cavity reflectivity with phase difference change curve, by out of phase
The absolute value summation of relative error at difference, obtains the corresponding total relative error magnitudes of the interference cavity reflectivity, then obtains total phase
To error amount with the change curve of interference cavity reflectivity；Total relative error magnitudes are returned with the change curve of interference cavity reflectivity
One change is handled, and takes the inverse of total relative error magnitudes after normalized as the sine K of interference fringesin, obtain interference item
The sine of line with interference cavity reflectivity change curve.
Further preferred embodiment, a kind of Varied clearance Fabry-Perot interferometer reflectivity determine method, feature
It is：In step 2, the monochromatic light interference fringe modulation degree of Varied clearance Fabry-Perot interference spectrum imaging system acquisition is established
The mathematical model of relationship is between Varied clearance Fabry-Perot interferometer interference cavity reflectivity：Interference fringe modulation degree
Further preferred embodiment, a kind of Varied clearance Fabry-Perot interferometer reflectivity determine method, feature
It is：In step 3, it is Z=K to take object functionsinM, in [0,1] interval range so that object function Z values are maximum dry
Interferometer interference cavity reflectance value is optimum reflectivity value Ropt。
Advantageous effect
The overall technology effect of the present invention is embodied in the following aspects.
(1) the monochromatic interference of light item that Varied clearance Fabry-Perot (F-P) interference spectrum imaging system of the invention obtains
The mathematical model of relationship between line sine and Varied clearance Fabry-Perot (F-P) interferometer interference cavity reflectivity, first, with
《High spectrum imaging method based on symmetric wedge interference cavity》It discusses and compares in text, determining Varied clearance F-P interferometer interference cavities
When optimum reflectivity value, it is contemplated that the influence of its monochromatic light interference fringe sine obtained to interference spectrum imaging system；Its
It is secondary, with《A compact LWIR hyperspectral system employing a microbolometer array
and a variable gap Fabry-Perot interferometer employed as a Fourier transform
spectrometer》Discussion in article is compared, and monochromatic light interference fringe sine and Varied clearance Fabry-Perot are clearly established
The mathematical model of relationship between sieve (F-P) interferometer interference cavity reflectivity.
(2) the monochromatic interference of light item that Varied clearance Fabry-Perot (F-P) interference spectrum imaging system of the invention obtains
The mathematical model of relationship between line modulation degree and Varied clearance Fabry-Perot (F-P) interferometer interference cavity reflectivity, first, with
《A compact LWIR hyperspectral system employing a microbolometer array and a
variable gap Fabry-Perot interferometer employed as a Fourier transform
spectrometer》Discussion in article is compared, and monochromatic light interference fringe modulation degree and Varied clearance Fabry-Perot are clearly established
The mathematical model of relationship between sieve (F-P) interferometer interference cavity reflectivity；Next, compared to《Based on symmetric wedge interference cavity
High spectrum imaging method》The polychromatic light interference fringe modulation degree discussed in text is dry with Varied clearance Fabry-Perot (F-P) interferometer
The mathematical relationship related between cavity reflection rate is compared, and monochromatic light interference fringe modulation degree and Varied clearance Fabry-Perot (F- are established
P) the mathematical relationship between interferometer interference cavity reflectivity, not only result formats are easily understood, but also mathematical model and Varied clearance
The F-P interferometer angles of wedge are unrelated, are only the functions of reflectivity, are easy to analyze.
(3) the monochromatic light interference fringe performance that Varied clearance Fabry-Perot interference spectrum imaging system of the invention obtains
It is the product of sine and modulation degree with the object function between its sine and modulation degree.It is right when target function value maximum
Varied clearance Fabry-Perot (F-P) the interferometer interference cavity reflectance value answered is optimum reflectivity value.Compared to《Based on symmetrical
The high spectrum imaging method of wedge-shaped interference cavity》Method is discussed in text, clearly proposes determining Varied clearance Fabry-Perot (F-P)
The specific criterion of interferometer reflection rate score.
Description of the drawings
Fig. 1 is the interference curve figure that monochromatic light interference light intensity changes with detector pixel position (phase difference).
Fig. 2 is monochromatic light interference light intensity and standard sine function error curve graph.
Fig. 3 is normalization error with interference cavity reflectivity changes curve graph.
Fig. 4 is influence curve figure of the interference cavity reflectivity to interference fringe modulation degree.
Fig. 5 is influence curve figure of the interference cavity reflectivity to transmission signal.
Specific implementation mode
Below in conjunction with the accompanying drawings and preferred embodiment the present invention is described in further detail.
Varied clearance Fabry-Perot interferometer reflectivity proposed by the present invention determines method, main to realize following three mesh
's：
1, the monochromatic light interference fringe that one Varied clearance Fabry-Perot (F-P) interference spectrum imaging system obtains is provided
The mathematical model of relationship between sine and Varied clearance Fabry-Perot (F-P) interferometer interference cavity reflectivity.
2, the monochromatic light interference fringe that one Varied clearance Fabry-Perot (F-P) interference spectrum imaging system obtains is provided
The mathematical model of relationship between modulation degree and Varied clearance Fabry-Perot (F-P) interferometer interference cavity reflectivity.
3, provide a Varied clearance Fabry-Perot interference spectrum imaging system obtain monochromatic light interference fringe performance with
Object function between its sine and modulation degree.
Specifically include following steps：
Step 1：Establish the monochromatic light interference fringe sine of Varied clearance Fabry-Perot interference spectrum imaging system acquisition
The mathematical model of relationship between Varied clearance Fabry-Perot interferometer interference cavity reflectivity；
Step 1.1：Establish the monochromatic light relative interference light intensity of Varied clearance Fabry-Perot interference spectrum imaging system acquisition
The mathematical model changed with phase difference：
Wherein Ii(λ) is the corresponding light intensity of incident light of monochromatic light that wavelength is λ, and I (λ) is Varied clearance Fabry-Perot Luo Gan
The monochromatic light relative interference light intensity of spectrum imaging system acquisition is related to, R is interference cavity reflectivity,For the phase between two interference lights
Difference：
X is distance of the horizontal direction interferometer away from optical axis, and α is the interferometer angle of wedge；
In [0,1] interval range, several interference cavity reflectivity values are set, by each interference cavity reflectivity values generation
Enter the mathematical model in this step, each interference cavity reflectivity corresponds to obtain a monochromatic light relative interference light intensity with phase difference variable
The curve of change；
Step 1.2：For each interference cavity reflectivity, a corresponding monochromatic light standard sine function curve is established：Its
The minimum and maximum amplitude of Plays the tracks of line voltage takes the corresponding list of interference cavity reflectivity obtained in step 1.1 respectively
The maximum value and minimum value of coloured light relative interference light intensity amplitude range, the phase difference constant interval of standard sine function curve and take
Value is identical as the calculated value in step 1.1；
Step 1.3：For each interference cavity reflectivity, the monochromatic light relative interference light intensity that calculating step 1.1 obtains is with phase
The relative error for the monochromatic light standard sine function curve that potential difference change curve is obtained with step 1.2 is with phase difference change curve；
Step 1.4：For the corresponding relative error of each interference cavity reflectivity with phase difference change curve, by out of phase
The absolute value summation of relative error at difference, obtains the corresponding total relative error magnitudes of the interference cavity reflectivity, then obtains total phase
To error amount with the change curve of interference cavity reflectivity；Total relative error magnitudes are returned with the change curve of interference cavity reflectivity
One change is handled, and takes the inverse of total relative error magnitudes after normalized as the sine K of interference fringesin, obtain interference item
The sine of line with interference cavity reflectivity change curve.
Step 2：Establish the monochromatic light interference fringe modulation degree of Varied clearance Fabry-Perot interference spectrum imaging system acquisition
The mathematical model of relationship between Varied clearance Fabry-Perot interferometer interference cavity reflectivity；
Interference fringe modulation degree M is defined as,
In formula, ImaxFor interference cavity transmitted light beam largest light intensity, IminFor interference cavity transmitted light beam minimum intensity of light.
Monochromatic light light intensity I and incident intensity I is obtained according to Varied clearance Fabry-Perot (F-P) interference spectrum imaging systemi
Relationship, relationship is between final modulation degree M and Varied clearance F-P interference cavity reflectivity R
Step 3：Mathematical model is obtained according to step 1 and step 2, with multiplying for monochromatic light interference fringe sine and modulation degree
Product is object function Z=KsinM, in [0,1] interval range so that the maximum interferometer interference cavity of object function Z values is anti-
Radiance rate value is optimum reflectivity value Ropt。
In the present embodiment, as shown in Figure 1, obtained according to Varied clearance Fabry-Perot (F-P) interference spectrum imaging system
The mathematical model that changes with phase difference of monochromatic light relative interference light intensity give any one interference in [0,1] interval range
Cavity reflection rate score can obtain the curve that a monochromatic light relative interference light intensity changes with phase difference by the mathematical model.
Black curve is standard sine curve of the amplitude in 0 to 1000 variation.Corresponding interference cavity is anti-from top to bottom for curve in figure
The rate of penetrating is the value changed at equal intervals every 0.2 from 0 to 1.The above results are the corresponding result of calculation of monochromatic light that wavelength is 10 μm.
As shown in Figure 2, it calculates under different reflectivity, in Fig. 1 between each interference curve and standard sine function curve
Error with phase difference change curve.Equally, corresponding interference cavity reflectivity is every from 0 to 1 to curve from top to bottom in figure
Every the value that 0.1 changes at equal intervals.
As shown in Figure 3, it is the relationship more clearly expressed between error amount and reflectivity, each curve in Fig. 2 is existed
The absolute value summation of corresponding error amount, the curve that can be obtained an error and change with phase difference are right at out of phase difference
It is normalized, and Fig. 3 can be obtained and show result.
As shown in Figure 4, Fig. 4 is according between formula (4) obtained F-P interference cavities reflectivity and interference fringe modulation degree
Relation curve.It can be seen that by the figure, interference cavity reflectivity is higher, and interference fringe modulation degree is better.
As shown in Figure 5, since modulation degree is the increasing function with reflectivity changes, to consider interference fringe
Sine and modulation degree, to choose best reflectance value, using the sine reciprocal for indicating interference fringe of curve shown in Fig. 3
Property, use KsinIt indicates, according to the definition of formula (5) object function, object function curve is drawn, as shown in figure Green curve.From
Fig. 5 can see, and when reflectance value is 0.37, target function value is up to 0.5997, i.e. optimum reflectivity value is 0.37.
Claims (4)
1. a kind of Varied clearance Fabry-Perot interferometer reflectivity determines method, it is characterised in that：Include the following steps：
Step 1：Establish monochromatic light interference fringe sine and the change of the acquisition of Varied clearance Fabry-Perot interference spectrum imaging system
The mathematical model of relationship between the Fabry-Perot interferometer interference cavity reflectivity of gap；
Step 2：Establish monochromatic light interference fringe modulation degree and the change of the acquisition of Varied clearance Fabry-Perot interference spectrum imaging system
The mathematical model of relationship between the Fabry-Perot interferometer interference cavity reflectivity of gap；
Step 3：Mathematical model is obtained according to step 1 and step 2, the product with monochromatic light interference fringe sine and modulation degree is
Object function, when target function value maximum, corresponding Varied clearance Fabry-Perot interferometer interference cavity reflectance value is best
Reflectance value.
2. a kind of Varied clearance Fabry-Perot interferometer reflectivity determines method according to claim 1, it is characterised in that：
In step 1, between establishing the monochromatic light interference fringe sine of Varied clearance Fabry-Perot interference spectrum imaging system acquisition and becoming
The process of the mathematical model of relationship is between gap Fabry-Perot interferometer interference cavity reflectivity：
Step 1.1：The monochromatic light relative interference light intensity of Varied clearance Fabry-Perot interference spectrum imaging system acquisition is established with phase
The mathematical model of potential difference variation：
Wherein Ii(λ) is the corresponding light intensity of incident light of monochromatic light that wavelength is λ, and I (λ) is Varied clearance Fabry-Perot interference spectrum
The monochromatic light relative interference light intensity that imaging system obtains, R are interference cavity reflectivity,For the phase difference between two interference lights：
X is distance of the horizontal direction interferometer away from optical axis, and α is the interferometer angle of wedge；
In [0,1] interval range, several interference cavity reflectivity values are set, each interference cavity reflectivity values are substituted into this
Mathematical model in step, each interference cavity reflectivity correspond to obtain what a monochromatic light relative interference light intensity changed with phase difference
Curve；
Step 1.2：For each interference cavity reflectivity, a corresponding monochromatic light standard sine function curve is established：It is got the bid
The minimum and maximum amplitude of quasi sinusoids curve takes the corresponding monochromatic light of interference cavity reflectivity obtained in step 1.1 respectively
The maximum value and minimum value of relative interference light intensity amplitude range, the phase difference constant interval and value of standard sine function curve with
Calculated value in step 1.1 is identical；
Step 1.3：For each interference cavity reflectivity, the monochromatic light relative interference light intensity that calculating step 1.1 obtains is with phase difference
The relative error for the monochromatic light standard sine function curve that change curve is obtained with step 1.2 is with phase difference change curve；
Step 1.4：For the corresponding relative error of each interference cavity reflectivity with phase difference change curve, at out of phase difference
Relative error absolute value summation, obtain the corresponding total relative error magnitudes of the interference cavity reflectivity, then obtain it is total opposite accidentally
Difference with interference cavity reflectivity change curve；Total relative error magnitudes are normalized with the change curve of interference cavity reflectivity
Processing, takes the inverse of total relative error magnitudes after normalized as the sine K of interference fringesin, obtain interference fringe
Sine with interference cavity reflectivity change curve.
3. a kind of Varied clearance Fabry-Perot interferometer reflectivity determines method according to claim 2, it is characterised in that：
In step 2, between establishing the monochromatic light interference fringe modulation degree of Varied clearance Fabry-Perot interference spectrum imaging system acquisition and becoming
The mathematical model of relationship is between gap Fabry-Perot interferometer interference cavity reflectivity：Interference fringe modulation degree
4. a kind of Varied clearance Fabry-Perot interferometer reflectivity determines method according to claim 3, it is characterised in that：
In step 3, it is Z=K to take object functionsinM, in [0,1] interval range so that the maximum interferometer of object function Z values is dry
It is optimum reflectivity value R to relate to cavity reflection rate valueopt。
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| CN111504609A (en) * | 2020-04-07 | 2020-08-07 | 西安应用光学研究所 | Wedge angle determination method for variable-gap Fabry-Perot interferometer |
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Application publication date: 20180803 |