CN104807616A - Spectralon diffuse reflection plate correcting method - Google Patents

Spectralon diffuse reflection plate correcting method Download PDF

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CN104807616A
CN104807616A CN201510200904.3A CN201510200904A CN104807616A CN 104807616 A CN104807616 A CN 104807616A CN 201510200904 A CN201510200904 A CN 201510200904A CN 104807616 A CN104807616 A CN 104807616A
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angle
data
zenith angle
diffuse reflector
formula
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CN104807616B (en
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方慧
张昭
张畅
杜朋朋
刘飞
何勇
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浙江大学
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Abstract

The invention discloses a Spectralon diffuse reflection plate correcting method. The method comprises the steps: 1) illuminating the Spectralon diffuse reflection plate from different zenith angles by a light source, and using the spectrograph to collect the corresponding reflection spectroscopic data from the different zenith angles and the azimuth angles; 2) intercepting the spectroscopic data within the valid wave band range from the reflection spectroscopic data, calculating the average value, and eliminating the spectroscopic data with relatively large difference; 3) calculating the residual sum of squares Rss of the residual spectroscopic data, determining the value of the most stable probe receiving zenith angle (thetar, degree), and establishing the relational expression of the random probe receiving zenith angle thetar and (thetar, degree); and 4) substituting the relational expression to the BRDF expression of the Spectralon diffuse reflection plate, and finishing the Spectralon diffuse reflection plate correction. The method is capable of using the known data of the Spectralon diffuse reflection plate to correct, calculating the universal expression of the probe receiving zenith angle orientation, and shortening the time for the follow-up test process.

Description

The bearing calibration of a kind of Spectralon diffuse reflector

Technical field

The present invention relates to optical property detection field, particularly relate to the bearing calibration of a kind of Spectralon diffuse reflector.

Background technology

When the BDRF optical characteristics of acquisition plane sample, incident radiation brightness value is difficult to measure, and needs to replace with on-gauge plate.Selection for on-gauge plate has following four standards:

1) for detecting radiometric diffuse reflection on-gauge plate, the BRDF characteristic of himself needs known;

2) on-gauge plate should have good approximate Lambertian characteristic, high reverse--bias value;

3), time as reference measurement, the size of on-gauge plate should be able to be detected the field angle of device (Field ofView, FOV) and cover;

4) the BRDF value stabilization at measuring process Plays plate need be ensured.

Spectralon diffuse reflector (Spectralon diffuse reflector) chemical composition is the teflon of sintering, when light source is close to 0 ° of zenith angle incidence, VIS, NIR wavelength band spectral ripple is little, also have simultaneously can process, weather proof, advantage capable of washing.

At present, existing for outdoor measurement standard plate universal method for correcting (Jackson, 1992; Bruegge, 2001).The Spectralon diffuse reflector that Experimental comparison's 11 kinds of materials are similar and 16 kinds of BaSO 4plate.Result shows, 11 kinds of Spectralon diffuse reflectors are at orientation/hemisphere, and orientation/orientation has less difference, propose general equation to Spectralon diffuse reflector, and BaSO 4plate is owing to differing greatly in experimentation, and universal equation is also inapplicable.In outdoor test, replace in test, needing the orientation/hemispherical reflectance acquired results of measurement more excellent with Spectralon diffuse reflector.

Summary of the invention

The present invention derives the Spectralon diffuse reflector bearing calibration being applicable to laboratory measurement planar sample reflection characteristic with distribution of bi directional reflectance function (BRDF), the data known with Spectralon diffuse reflector correct, and propose and receive the general expression formula in zenith angle orientation at detector, the time for follow-up test processes shrink.

Concrete technical scheme of the present invention is as follows:

The bearing calibration of a kind of Spectralon diffuse reflector, comprises the following steps:

1) light source never irradiates Spectralon diffuse reflector with zenith angle, utilizes spectrometer never to gather corresponding reflected spectrum data with zenith angle and position angle;

2) in described reflected spectrum data, intercept the spectroscopic data in significant wave segment limit, and average, reject the spectroscopic data that difference is relatively large;

3) residual sum of squares (RSS) Rss is asked to remaining spectroscopic data, determine that the most stable detector accepts zenith angle θ r, degreevalue, and set up any detector and accept zenith angle θ rwith θ r, degreerelational expression;

4) relational expression is substituted into the BRDF expression formula of Spectralon diffuse reflector, complete Spectralon diffuse reflector and correct.

When carrying out reflected spectrum data collection, the position angle controlling light source is 0 °, it is 0 °, 10 °, 30 ° and 45 ° that zenith angle sets gradually, detector is utilized to gather one by one at each zenith angle place of light source, zenith angle from 0 ° ~ 70 ° every 10 ° of collections, position angle from 0 ° ~ 360 ° every 10 ° of collections.

For eliminating surround lighting to the impact of measurement data, need to close light source, control detector and again gather corresponding surround lighting modal data with equal zenith angle and position angle, and the original light source data gathered under light source and surround lighting modal data are done difference process, obtain step 1) in reflected spectrum data.

In step 2) in, according to instrument performance and experimental study content, select the spectroscopic data of suitable wavelength band, as the spectroscopic data in described significant wave segment limit, the significant wave segment limit usually selected is visible ray and near infrared light wave band.

In step 2) in, the acquisition interval according to detector zenith angle is divided into groups to spectroscopic data, calculates the mean value often organizing data, and carries out secondary rejecting process to spectroscopic data.

Described secondary is rejected and is treated to: utilize formula (1) tentatively to reject spectroscopic data, remaining spectroscopic data is averaged, and recycling formula (2) rejects process again to remaining spectroscopic data;

| 100 &times; L n 1 ( i , j ) - M n 1 ( i , j ) M n 1 ( i , j ) | < 25 - - - ( 1 )

| 100 &times; L n 2 ( i , j ) - M n 2 ( i , j ) M n 2 ( i , j ) | < 15 - - - ( 2 )

In formula, L, M are respectively raw data in each group and corresponding statistical average, and n represent and divides class value according to detector zenith angle institute, and n1, n2 are respectively for the first time, data matrix for the second time, and i, j are respectively azimuth value and wavelength.

Described step 3) in ask the formula of residual sum of squares (RSS) Rss to be,

Rss = &Sigma; i = 1 m &Sigma; j = 1 k ( L n 3 ( i , j ) - M n 3 ( i , j ) M n 3 ( i , j ) ) 2 m &times; k

In formula, L, M are respectively secondary and reject raw data after process in each group and corresponding statistical average, n3 is the spectrum data matrix after secondary rejects process, and i, j are respectively azimuth value and wavelength, m, k are respectively data secondary and reject rear detector position angle and wave band number.

In step 3) in, be that stable detector receives zenith angle with the collection zenith angle of the little correspondence of residual sum of squares (RSS) Rss numerical value difference.

The step of asking for of the BRDF expression formula of described Spectralon diffuse reflector comprises:

4.1, initial BRDF expression formula is determined

f r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = &rho; H &times; dT ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) / cos &theta; r &Integral; dT ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) d&omega; r - - - ( 3 )

In formula, θ ifor light source zenith angle, φ ifor light source azimuth angle, θ rfor detector zenith angle, φ rfor detector position angle, λ represents wavelength, d ω rfor reflected radiation solid angle, ρ hfor the DHRF of Spectralon diffuse reflector, dT reffor the value of detector under any zenith angle;

4.2, the correction relationship formula between the image data of the most stable zenith angle and the image data of any zenith angle is set up,

dT refiirr,λ)=dT c,refii,c,φ r,λ)·f(cosθ r) (4)

4.3, formula (4) is substituted into initial BRDF expression formula (3), calculate the BRDF expression formula of the Spectralon diffuse reflector after correction.

Principle of the present invention is as follows:

Distribution of bi directional reflectance function (BRDF) is defined as the reflection width brightness infinitesimal amount dL from sample surface specific direction rwith the ratio dE of surface irradiation degree infinitesimal amount i, use f rrepresent, see Fig. 1.Its expression formula is shown in 1:

f r ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = dL r ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) dE i ( &theta; i , &phi; i , &lambda; ) - - - ( 5 )

Find out thus, f rvalue and light source zenith angle θ i, position angle φ i, detector zenith angle θ r, position angle φ r, wavelength X is relevant, and span is (0 ,+∞), and dimension is sr -1; And dE ithen one and θ i, φ i, the three-variable function that λ is relevant;

In order to computational reflect light is at the integrated value of sample space episphere, introduce the directed hemispherical reflectivity factor (DHRF, ρ), its expression formula is (6):

DHRF(θ ii,λ)=∫f riirr,λ)cosθ rr(6)

In formula, d ω rfor reflected radiation solid angle, d ω r=sin θ rd θ rd φ r; The span of DHRF is (0,1), because the DHRF of Spectralon diffuse reflector is demarcated, namely can be used for asking f according to formula (6) r.

In the ideal situation, for the little incidence that takes measurement of an angle and observed bearing, its f rvalue is the definite value π irrelevant with direction wavelength -1but, under the actual experiment state of large measured angular, need accurate test to measure f rvalue is with the stability of corrective system; Therefore, formula (5) and formula (6) simultaneous can be obtained the DHRF (ρ of Spectralon diffuse reflector h) expression formula is as follows:

&rho; H ( &theta; i , &phi; i , &lambda; ) = &Integral; dL r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) dE i ( &theta; i , &phi; i , &lambda; ) cos &theta; r d&omega; r - - - ( 7 )

Because the value of the infinitesimal amount and reflection direction that incide sample surface irradiance has nothing to do, therefore obtains formula (8):

dE i ( &theta; i , &phi; i , &lambda; ) = 1 &rho; H &Integral; dL r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) cos &theta; r d&omega; r - - - ( 8 )

Formula (8) is substituted in formula (5), the f of blank can be obtained rvalue:

f r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = &rho; H &times; dL r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) &Integral; dL r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) cos &theta; r d &omega; r - - - ( 9 )

Light source incidence is to infinitesimal face, Lambertian surface dA back reflection to (θ r, φ r) d ω on direction rthe reflection irradiance expression formula of unit solid angle such as formula (10):

r=dL riirr,λ)cosθ rdAdω r(10)

dT ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = d&Phi; r d&omega; r - - - ( 11 )

D Φ in formula (11) r/ d ω ravailable experimental measured value replaces; By formula (9), (10) and (11) simultaneous, just obtains f r, refwith the relational expression (12) of measured value: f r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = &rho; H &times; dT ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) / cos &theta; r &Integral; dT ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) d &omega; r - - - ( 12 )

In experiment, need obtain the reflection width brightness at any point of Spectralon diffuse reflector, Spectralon diffuse reflector measured value meets formula (13) under desirable measuring condition:

dT refiirr,λ)=dT c,refii,c,φ r,λ)·cosθ r(13)

In formula, dT c, reffor the value of detector under certain day drift angle; DT reffor the value of detector under any zenith angle; In actual measurement, due to the moving problem of manual operation error, optical fiber, cannot directly use this formula; For simplified measurement workload, shorten the total duration often surveying experiment, utilize a certain specific angle value dT c, refcalculate dT under arbitrary zenith angle ref, specifically comprise: f r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = &rho; H &pi; - - - ( 14 )

The signal dT gathered c, refwith cos θ rfor polynomial revise relation:

dT refiirr,λ)=dT c,refii,c,φ r,λ)·f(cosθ r) (15)

Then the BRDF expression formula of Spectralon diffuse reflector is f r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = &rho; H &times; f ( cos &theta; r ) cos &theta; r &Integral; f ( cos &theta; r ) d&omega; r - - - ( 16 )

In practical operation, first determine detector the best reflection zenith angle (θ r, degree), all the other angle measurement are with θ r, degreefor standard normalization; Set up arbitrarily angled θ rmeasured value reflect zenith angle θ with best r, degreerelational expression f (the cos θ of measured value r).

This relational expression is brought into formula (16), Spectralon diffuse reflector BRDF expression formula after can being simplified, this is the end result of Spectralon diffuse reflector antidote proposed by the invention, utilize this achievement greatly can simplify Spectralon diffuse reflector correcting process, solve original Measures compare complicated, the problem that the error of calculation is larger, is easy to realize and operation, greatly reduces experiment required time.

Accompanying drawing explanation

Fig. 1 is reflection detection geometric representation;

Fig. 2 is θ iwhen=45 ° of segment limits are 450-994nm, θ rat the scale-up factor of different angles;

Fig. 3 is Spectralon diffuse reflector 4 light source incidence angles, the original value L of wavelength 800nm r, ref(left column) and ratio proccessing value (right row); Pentagram is light source incidence angle;

Cosine function fitted figure when Fig. 4 is 800nm under 4 light source incidence angles;

L when Fig. 5 is 800nm after the correction of Spectralon diffuse reflector under 4 light source incidence angles r, refvalue, red pentagram is light source incidence angle.

Embodiment

Illustrate that the invention will be further described below in conjunction with accompanying drawing, concrete steps are as follows:

1) choosing the Spectralon diffuse reflector of sea blue luxuriant and rich with fragrance optics, in 250-2500nm wavelength band, except 250nm, 2400nm, 2450nm and 2500nm, take 50nm as the ρ relative to Lambertian body of step-length, 8 ° of zenith angle incidences hvalue is all through check and correction, and wherein minimum value is 0.992, and maximal value is 0.998.

2) open light source, spectrometer, stablize more than 15min.

3) adjusting light source azimuth angle is 0 °, and zenith angle is fixed as 0 °, 10 °, 30 ° and 45 ° successively; For avoiding CCD to expose, the integral time that setting is optimum.

4) manual rotation control detector, make its zenith angle from 0 ° ~ 70 ° every 10 ° of collections, position angle from 0 ° ~ 360 ° every 10 ° of collections.

5) Spectralon diffuse reflector demarcates 252(light source θ i at every turn when being 0 °, and detector φ i is 10 ° ~ 70 °) or 288 curves be about 20min, replication 20 times.

6) dark current 10 times are measured, the impact of dark current in deduction raw data.

When light source is in different incidence zenith angle, because pick-up probe and light source interact, make sample platform occur capture-effect, table 1 lists concrete angle, adopts method of interpolation or scalping method in subsequent treatment.

Main the blocking a little or non-measuring point of table 1 optical light source and detector interaction

In addition, the impact of Curvature varying during error and optical fiber moving in order to the rotary manual operation that rectifies an instrument, each incidence zenith angle revision test 5 times, each group data handling procedure is as follows:

1) intercept wavelength band in the data of 450-994nm, be divided into 7 groups or 8 groups according to the acquisition interval of detector zenith angle according to corresponding spectrum number (252 or 288).

2) calculate the mean value often organizing data according to formula (17) and (18), rejected by secondary when measured value does not meet formula, so relatively steady and close data are retained.

| 100 &times; L n 1 ( i , j ) - M n 1 ( i , j ) M n 1 ( i , j ) | < 25 - - - ( 17 )

| 100 &times; L n 2 ( i , j ) - M n 2 ( i , j ) M n 2 ( i , j ) | < 15 - - - ( 18 )

In formula, L, M are respectively raw data and statistical average, and n represents and divide class value according to detector zenith angle institute, and n1, n2 are respectively for the first time, data matrix for the second time, and i, j are respectively azimuth value and wavelength.

3) residual sum of squares (RSS) Rss (formula 19) is used for determining the most stable detector incidence zenith angle (θ r, degree) value.

Rss = &Sigma; i = 1 m &Sigma; j = 1 k ( L n 3 ( i , j ) - M n 3 ( i , j ) M n 3 ( i , j ) ) 2 m &times; k - - - ( 19 )

In formula, m, k are respectively data secondary and reject rear detector position angle and wave band number.

4) the best incidence zenith angle θ of detector is determined r, degreeafter, the value of other angle is with θ r, degreefor standard normalization, set up θ rwith θ r, degreerelational expression.

Table 2 lists light source 4 different incidence angles degree θ ishi Butong detector zenith angle θ raverage Rss value, Rss mean value is all less than 0.075.In measuring for 20 times, Rss is with θ rincrease and increase gradually.θ rduring=10-30 °, its value is less than 0.05.Select θ r, degree=30 ° is best incidence zenith angle, reduces error of fitting.

The different θ of table 2 Spectralon diffuse reflector iθ under angle rrss average

Repeat step 4) process, Fig. 2 gives the (θ that wavelength band is 450-994nm i, φ i, φ r)=(45 °, 0 °, 0 °) scalefactor value.In different-waveband, θ r=0 ° and θ r=10 ° all have less floating and similar trend, and show that low-angle is relative to 30 °, its measured value is close to each other; Work as θ rduring increase, scale-up factor reduces more, and minimum value is 0.4.θ rscale-up factor be an amount irrelevant with wavelength, therefore Fig. 3 gives the episphere distribution of Spectralon diffuse reflector under single wavelength.

Fig. 3 illustrates Spectralon diffuse reflector 0 °, 10 °, 30 ° and 45 ° of light source incidence zenith angles, the original value (left side) under 800nm wavelength and the diffusion figure with the best zenith angle 30 ° of the detector ratio Distribution value (right side) that is benchmark hemisphere on the sample surface.θ r=0 °, the highest and close to each other when 10 °, be 1.19 times; θ rhaving minimum when=70 °, is 0.24 times.Because integral time is different, L r, refat θ ithe value of=45 ° is lower than θ i=0 °, be therefore better than the comparison between original value using scale-up factor as standard.θ iwhen=10 °, figure medium value line concavo-convex is because the error when curvature moving of optical fiber or manual operation causes.

According to Lambert cosine law (Lambert ' s cosine law), measured value in test is revised.According to Different Light incident angle, detector zenith angle grouping as input parameter, after compared for polynomial expression, cosine function fitting effect, find cosine function closer to.When Fig. 4 gives 800nm, Spectralon diffuse reflector is at different θ idistribute after the cosine function matching of angle.Compare Fig. 3, level line is more level and smooth, and the correction for algorithm is more accurate.

In like manner demonstrate 550nm according to cosine function relationship formula, the Spectralon diffuse reflector episphere distribution of 715nm.Result shows f (cos θ r)=Acos θ rthe coefficient value change of+B is little, and A value is approximately 1.39, B value and is approximately-0.21, now R 2reach 0.998.Like this, ask the mean value of 400-994nm as the universal equation of each angle.

Scale-up factor and θ under table 3 four incidence zenith angle rfuntcional relationship

Wherein, Y represents scale-up factor, and X represents θ r(Circular measure).

Table 3 analyzes the non-ideal optical character of Spectralon diffuse reflector in systematic survey.Test shows that the fitting effect of a cosine function is optimum, under four incident angles, and its R 2value reaches 0.999, RMSE value then lower than 0.110.A value is from 1.33 (θ i=0 °) change to 1.44 (θ i=45 °), B value is then from-0.16 (θ i=45 °) change to-0.24 (θ i=0 °).Because under each angle, coefficient value is close to each other, according to the operation steps of trimming process, general cosine function formula can be derived.Each measured value unification under four angles is shown in Fig. 4 and Fig. 5 as input, and after exporting, A, B value is in the middle of numerical value above, R 2be 0.9982, RMSE be 0.0134.Finally, θ i=0 ° ~ 45 ° general purpose function expression formulas are:

Y=1.3938cosX-0.2127 (20)

Formula (20) is f (cos θ r) fitting formula, carrying it into formula (16), can to obtain the final expression formula of Spectralon diffuse reflector as follows. f r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = &rho; H &times; ( 1.3939 cos &theta; r - 0.2127 ) cos &theta; r &Integral; ( 1.3939 cos &theta; r - 0.2127 ) d&omega; r - - - ( 21 )

When Fig. 5 gives 800nm, Spectralon diffuse reflector is at different θ il after correction under angle r, refdistribution value figure, this figure are the result figure of Spectralon diffuse reflector bearing calibration in the present invention.

Claims (9)

1. the bearing calibration of Spectralon diffuse reflector, is characterized in that, comprises the following steps:
1) light source never irradiates Spectralon diffuse reflector with zenith angle, utilizes spectrometer never to gather corresponding reflected spectrum data with zenith angle and position angle;
2) in described reflected spectrum data, intercept the spectroscopic data in significant wave segment limit, and average, reject the spectroscopic data that difference is relatively large;
3) residual sum of squares (RSS) Rss is asked to remaining spectroscopic data, determine that the most stable detector accepts zenith angle θ r, degreevalue, and set up any detector and accept zenith angle θ rwith θ r, degreerelational expression;
4) relational expression is substituted into the BRDF expression formula of Spectralon diffuse reflector, complete Spectralon diffuse reflector and correct.
2. Spectralon diffuse reflector bearing calibration as claimed in claim 1, it is characterized in that, in step 1) in, the position angle controlling light source is 0 °, it is 0 °, 10 °, 30 ° and 45 ° that zenith angle sets gradually, utilize detector to gather one by one at each zenith angle place of light source, zenith angle from 0 ° ~ 70 ° every 10 ° of collections, position angle from 0 ° ~ 360 ° every 10 ° of collections.
3. Spectralon diffuse reflector bearing calibration as claimed in claim 2, it is characterized in that, close light source, control detector and again gather corresponding surround lighting modal data with equal zenith angle and position angle, and the original light source data gathered under light source and surround lighting modal data are done difference process, obtain step 1) in reflected spectrum data.
4. Spectralon diffuse reflector bearing calibration as claimed in claim 1, it is characterized in that, described significant wave segment limit is visible ray and near infrared light wave band.
5. Spectralon diffuse reflector bearing calibration as claimed in claim 1, it is characterized in that, in step 2) in, the acquisition interval according to detector zenith angle is divided into groups to spectroscopic data, calculate the mean value often organizing data, and secondary rejecting process is carried out to spectroscopic data.
6. Spectralon diffuse reflector bearing calibration as claimed in claim 5, it is characterized in that, described secondary is rejected and is treated to: utilize formula (1) tentatively to reject spectroscopic data, remaining spectroscopic data is averaged, and recycling formula (2) rejects process again to remaining spectroscopic data;
| 100 &times; L n 1 ( i , j ) - M n 1 ( i , j ) M n 1 ( i , j ) | < 25 - - - ( 1 )
| 100 &times; L n 2 ( i , j ) - M n 2 ( i , j ) M n 2 ( i , j ) | < 15 - - - ( 2 )
In formula, L, M are respectively raw data in each group and corresponding statistical average, and n represent and divides class value according to detector zenith angle institute, and n1, n2 are respectively for the first time, data matrix for the second time, and i, j are respectively azimuth value and wavelength.
7. Spectralon diffuse reflector bearing calibration as claimed in claim 6, is characterized in that, described step 3) in ask the formula of residual sum of squares (RSS) Rss to be,
Rss = &Sigma; i = 1 m &Sigma; j = 1 k ( L n 3 ( i , j ) - M n 3 ( i , j ) M n 3 ( i , j ) ) 2 m &times; k
In formula, L, M are respectively secondary and reject raw data after process in each group and corresponding statistical average, n3 is the spectrum data matrix after secondary rejects process, and i, j are respectively azimuth value and wavelength, m, k are respectively data secondary and reject rear detector position angle and wave band number.
8. Spectralon diffuse reflector bearing calibration as claimed in claim 7, is characterized in that, in step 3) in, be that stable detector receives zenith angle with the collection zenith angle of the little correspondence of residual sum of squares (RSS) Rss numerical value difference.
9. Spectralon diffuse reflector bearing calibration as claimed in claim 1, it is characterized in that, the step of asking for of the BRDF expression formula of described Spectralon diffuse reflector comprises:
4.1, initial BRDF expression formula is determined
f r , ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) = &rho; H &times; d T ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) / cos &theta; r &Integral; d T ref ( &theta; i , &phi; i , &theta; r , &phi; r , &lambda; ) d &omega; r - - - ( 3 )
In formula, θ ifor light source zenith angle, φ ifor light source azimuth angle, θ rfor detector zenith angle, φ rfor detector position angle, λ represents wavelength, d ω rfor reflected radiation solid angle, ρ hfor the DHRF of Spectralon diffuse reflector, dT reffor the value of detector under any zenith angle;
4.2, the correction relationship formula between the image data of the most stable zenith angle and the image data of any zenith angle is set up,
dT refiirr,λ)=dT c,refii,c,φ r,λ)·f(cosθ r) (4)
4.3, formula (4) is substituted into initial BRDF expression formula (3), calculate the BRDF expression formula of the Spectralon diffuse reflector after correction.
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