CN104807616B - A kind of Spectralon diffusing reflections plate bearing calibration - Google Patents

Abstract

The invention discloses a kind of Spectralon diffusing reflections plate bearing calibration, including step：1) light source never irradiates Spectralon diffusing reflection plates with zenith angle, and never corresponding reflected spectrum data is gathered with zenith angle and azimuth using spectrometer；2) spectroscopic data in effective wavelength band is intercepted from the reflected spectrum data, and is averaged, reject the relatively large spectroscopic data of difference；3) residual sum of squares (RSS) Rss is asked to remaining spectroscopic data, determines that most stable of detector receives zenith angle θ_r,degreeValue, and set up any detector and receive zenith angle θ_rWith θ_r,degreeRelational expression；4) relational expression is substituted into the BRDF expression formulas of Spectralon diffusing reflection plates, the correction of Spectralon diffusing reflections plate is completed.The present invention is corrected using data known to Spectralon diffusing reflection plates, and calculates the general expression formula of detector reception zenith angular range, is that follow-up test process shortens the time.

Description

A kind of Spectralon diffusing reflections plate bearing calibration

Technical field

The present invention relates to optical property detection field, more particularly to a kind of Spectralon diffusing reflections plate bearing calibration.

Background technology

In the BDRF optical characteristics of acquisition plane sample, incident radiation brightness value is difficult to determine, it is necessary to use on-gauge plate generation Replace.There is following four standard for the selection of on-gauge plate：

1) for detecting radiometric diffusing reflection on-gauge plate, the BRDF characteristics of its own need known；

2) on-gauge plate should have good approximate Lambertian characteristics, high reflection value；

3) when as reference measurement, the size of on-gauge plate should be able to be by the angle of visual field (Field of View, FOV) of detector Covering；

4) the BRDF value stabilizations in measurement process Plays plate need to be ensured.

Spectralon diffusing reflections plate (Spectralon diffusing reflections plate) chemical composition is the polytetrafluoroethylene (PTFE) of sintering, works as light Source is close to 0 ° of zenith angle incidence, and VIS, NIR wavelength band spectral ripple are small, at the same also have can process, it is weather proof, capable of washing Advantage.

At present, for outdoor measurement standard plate universal method for correcting (Jackson, 1992；Bruegge,2001).It is real Test and compared for 11 kinds of similar Spectralon diffusing reflections plates of material and 16 kinds of BaSO₄Plate.Result shows, 11 kinds of Spectralon Diffusing reflection plate has less difference, Spectralon diffusing reflection plates is proposed general in orientation/hemisphere, orientation/orientation Equation, and BaSO₄Due to being differed greatly in experimentation, universal equation is not applied to simultaneously plate.In outdoor test, use Spectralon diffusing reflections plate replaces needing the orientation/hemispherical reflectance acquired results of measurement more excellent in experiment.

The content of the invention

The present invention is derived suitable for laboratory measurement planar sample reflection characteristic with distribution of bi directional reflectance function (BRDF) Spectralon diffusing reflection plate bearing calibrations, be corrected with data known to Spectralon diffusing reflection plates, and propose The general expression formula of zenith angular range is received in detector, is that follow-up test process shortens the time.

Concrete technical scheme of the present invention is as follows：

A kind of Spectralon diffusing reflections plate bearing calibration, comprises the following steps：

1) light source never irradiates Spectralon diffusing reflection plates with zenith angle, using spectrometer never with zenith angle and orientation Angle gathers corresponding reflected spectrum data；

2) spectroscopic data in effective wavelength band is intercepted from the reflected spectrum data, and is averaged, it is poor to reject Different relatively large spectroscopic data；

3) residual sum of squares (RSS) Rss is asked to remaining spectroscopic data, determines that most stable of detector receives zenith angle θ_r,degree Value, and set up any detector and receive zenith angle θ_rWith θ_r,degreeRelational expression；

4) relational expression is substituted into the BRDF expression formulas of Spectralon diffusing reflection plates, Spectralon diffusing reflections are completed Plate is corrected.

Carry out reflected spectrum data gather when, control light source azimuth be 0 °, zenith angle set gradually for 0 °, 10 °, 30 ° and 45 °, gathered one by one at each zenith angle of light source using detector, zenith angle is from 0 °~70 ° every 10 ° of collections, side Parallactic angle is from 0 °~360 ° every 10 ° of collections.

To eliminate influence of the ambient light to measurement data, it is necessary to close light source, control detector is again with equal zenith Angle and azimuth gather corresponding ambient light spectrum data, and the original light source data that will be gathered under light source are done with ambient light spectrum data Difference treatment, obtain step 1) in reflected spectrum data.

In step 2) in, according to instrument performance and experimental study content, the spectroscopic data of suitable wavelength band is selected, as Spectroscopic data in effective wavelength band, the effective wavelength band for generally selecting is visible ray and near infrared light wave band.

In step 2) in, the acquisition interval according to detector zenith angle is grouped to spectroscopic data, calculates every group of data Average value, and secondary rejecting treatment is carried out to spectroscopic data.

Described secondary rejecting is processed as：Spectroscopic data is tentatively rejected using formula (1), remaining spectroscopic data Average, recycle formula (2) that the treatment of rejecting again is carried out to remaining spectroscopic data；

In formula, L, M is respectively initial data and corresponding statistical average in each group, and n is represented according to detector zenith Angle is grouped value, n1, and n2 is respectively first time, second data matrix, and i, j is respectively azimuth value and wavelength.

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

In formula, L, M is respectively after secondary rejecting is processed initial data and corresponding statistical average in each group, and n3 is two Spectrum data matrix after secondary rejecting treatment, i, j is respectively azimuth value and wavelength, m, after k is respectively the secondary rejecting of data Detector azimuth and wave band number.

In step 3) in, connect with the detector that the small corresponding collection zenith angle of residual sum of squares (RSS) Rss numerical value differences is stabilization Receive zenith angle.

The step of asking for of the BRDF expression formulas of the Spectralon diffusing reflections plate includes：

4.1st, initial BRDF expression formulas are determined

In formula, θ_iIt is light source zenith angle, φ_iIt is light source azimuth angle, θ_rIt is detector zenith angle, φ_rIt is detector orientation Angle, λ represents wavelength, d ω_rIt is reflected radiation solid angle, ρ_HIt is the DHRF of Spectralon diffusing reflection plates, dT_refFor detector exists Value under any zenith angle；

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

dT_ref(θ_i,φ_i,θ_r,φ_r, λ) and=dT_c,ref(θ_i,φ_i,c,φ_r,λ)·f(cosθ_r) (4)

4.3rd, formula (4) is substituted into initial BRDF expression formulas (3), is calculated the Spectralon diffusing reflection plates after correction BRDF expression formulas.

Principle of the invention is as follows：

The definition of distribution of bi directional reflectance function (BRDF) is the reflection width brightness infinitesimal amount from sample surface specific direction dL_rWith the ratio dE of surface irradiation degree infinitesimal amount_i, use f_rRepresent, see Fig. 1.Its expression formula is shown in 1：

It is therefore seen that, f_rValue and light source zenith angle θ_i, azimuth φ_i, detector zenith angle θ_r, azimuth φ_r, wavelength X Relevant, span is (0 ,+∞), and dimension is sr^-1；And dE_iIt is then one and θ_i, φ_i, the three-variable function of λ correlations；

In order to calculate integrated value of the reflected light in sample space episphere, introduce the orientation hemispherical reflectivity factor (DHRF, ρ), its expression formula is (6)：

DHRF(θ_i,φ_i, λ) and=∫ f_r(θ_i,φ_i,θ_r,φ_r,λ)cosθ_rdω_r (6)

In formula, d ω_rIt is reflected radiation solid angle, d ω_r=sin θ_rdθ_rdφ_r；The span of DHRF is (0,1), because The DHRF of Spectralon diffusing reflection plates has been calibrated, and is that can be used to seek f according to formula (6)_r。

In the ideal situation, the incidence for small measurement angle and observed bearing, its f_rValue is unrelated with direction wavelength Definite value π^-1But, under the actual experiment state of big measurement angle, it is necessary to accurate test measurement f_rValue is correcting the steady of system It is qualitative；Therefore, formula (5) and formula (6) simultaneous can obtain the DHRF (ρ of Spectralon diffusing reflection plates_H) expression formula is as follows:

Because the infinitesimal amount for inciding sample surface irradiation level is unrelated with the value of reflection direction, therefore obtain formula (8)：

By in formula (8) substitution formula (5), the f of blank can be obtained_rValue：

Light source incidence is to Lambertian surfaces infinitesimal face dA back reflections to (θ_r, φ_r) d ω on direction_rUnit solid angle Reflection irradiation level expression formula such as formula (10)：

dΦ_r=dL_r(θ_i,φ_i,θ_r,φ_r,λ)cosθ_rdAdω_r (10)

D Φ in formula (11)_r/dω_rCan be replaced with experimental measurements；By formula (9), (10) and (11) simultaneous is just obtained f_r,refWith the relational expression (12) of measured value：

In experiment, the reflection width brightness at any point of Spectralon diffusing reflections plate need to be obtained, Spectralon is unrestrained anti- Penetrate plate measured value and meet formula under preferable measuring condition（13）：

dT_ref(θ_i,φ_i,θ_r,φ_r,λ)=dT_c,ref(θ_i,φ_i,c,φ_r,λ)·cosθ_r（13）

In formula, dT_c,refIt is value of the detector under specific zenith angle；dT_refIt is value of the detector under any zenith angle； In actually measurement, due to manual operation error, the moving problem of optical fiber, it is impossible to directly use the formula；To simplify measurement work The total duration of experiment is often surveyed in amount, shortening, using by a certain specific angle value dT_c,refCalculate dT under any zenith angle_ref, specifically Including：

The signal dT of collection_c,refWith cos θ_rIt is multinomial correction relationship：

dT_ref(θ_i,φ_i,θ_r,φ_r,λ)=dT_c,ref(θ_i,φ_i,c,φ_r,λ)·f(cosθ_r) （15）

Then the BRDF expression formulas of Spectralon diffusing reflections plate are

In practical operation, it is first determined detector most preferably reflects zenith angle (θ_r,degree), remaining angle measurement with θ_r,degreeFor standard is normalized；Set up arbitrarily angled θ_rMeasured value and optimal reflection zenith angle θ_r,degreeThe relation table of measured value Up to formula f (cos θ_r)。

Bring this relational expression into formula（16）, you can the Spectralon diffusing reflection plates BRDF expression after being simplified Formula, this is the end result of Spectralon diffusing reflection plate antidotes proposed by the invention, can be very big using this achievement Simplify Spectralon diffusing reflection plate correcting process, solve that original method is more complicated, the larger problem of calculation error, it is easy to Realize and operate, the time required to substantially reducing experiment.

Brief description of the drawings

Fig. 1 is reflection detection geometric representation；

Fig. 2 is θ_iWhen=45 ° of segment limits are 450-994nm, θ_rIn the proportionality coefficient of different angles；

Fig. 3 is 4 light source incidence angles of Spectralon diffusing reflections plate, the original value L of wavelength 800nm_r,ref(left column) and Ratio proccessing value (right row)；Five-pointed star 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 correction of the Spectralon diffusing reflections plate under 4 light source incidence angles_r,refValue, it is red Color five-pointed star is light source incidence angle.

Specific embodiment

The invention will be further described for explanation below in conjunction with the accompanying drawings, comprises the following steps that：

1）Sea blue luxuriant and rich with fragrance optical Spectralon diffusing reflections plate, in 250-2500nm wavelength bands, removes in selection Outside 250nm, 2400nm, 2450nm and 2500nm, with 50nm as step-length, 8 ° of zenith angles it is incident relative to Lambertian bodies ρ_HValue has passed through check and correction, and wherein minimum value is 0.992, and maximum is 0.998.

2）Open light source, spectrometer, stabilization more than 15min.

3）Adjustment light source azimuth angle is 0 °, and zenith angle is fixed as 0 °, 10 °, 30 ° and 45 ° successively；To avoid CCD from exposing, if The fixed optimal time of integration.

4）Manual rotation controls detector, makes its zenith angle from 0 °~70 ° every 10 ° of collections, and azimuth is from 0 °~360 ° Every 10 ° of collections.

5）Spectralon diffusing reflections plate demarcates 252 every time（When light source θ i are 0 °, detector φ i are 10 °~70 °）Or 288 curve about 20min, replication 20 times.

6）Determine dark current 10 times, deduct the influence of dark current in initial data.

When light source is in different incidence zenith angles, because pick-up probe and light source interact so that sample platform goes out Existing shadowing effect, table 1 lists specific angle, and interpolation method or scalping method are used in subsequent treatment.

The optical light source and detector of table 1 interacts main blocking a little or non-measuring point

The influence of Curvature varying when in addition, for the error and optical fiber moving of the rotary manual operation that rectifies an instrument, Experiment 5 times is repeated in each incidence zenith angle, each group of data handling procedure is as follows：

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

2) every group of average value of data is calculated according to formula (17) and (18), it is i.e. secondary when measured value is unsatisfactory for formula Reject, so relatively steady and close data are retained.

In formula, L, M are respectively initial data and statistical average, and n is represented and is grouped value according to detector zenith angle, n1, N2 is respectively first time, second data matrix, and i, j is respectively azimuth value and wavelength.

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

In formula, m, k is respectively detector azimuth and wave band number after the secondary rejecting of data.

4) the optimal incidence zenith angle θ of detector is determined_r,degreeAfterwards, the value of other angles is with θ_r,degreeFor standard is normalized, Set up θ_rWith θ_r,degreeRelational expression.

Table 2 lists 4 incidence angles degree θ of light source_iShi Butong detector zenith angles θ_rAverage Rss values, Rss is average Value is respectively less than 0.075.In 20 measurements, Rss is with θ_rIncrease and gradually increase.θ_rIts value is less than 0.05 at=10-30 °.Selection θ_r,degree=30 ° is optimal incidence zenith angle, reduces error of fitting.

The Spectralon diffusing reflections plate difference θ of table 2_iθ under angle_rRss averages

Repeat step 4) process, it is (the θ of 450-994nm that Fig. 2 gives wavelength band_i, φ_i, φ_r45 °, 0 °, 0 ° of)=() Scalefactor value.In different-waveband, θ_r=0 ° and θ_r=10 ° have it is less floating and trend is similar, show that low-angle is relative In 30 °, its measured value is close to each other；Work as θ_rDuring increase, proportionality coefficient reduction is more, and minimum value is 0.4.θ_rProportionality coefficient be One amount unrelated with wavelength, therefore Fig. 3 gives the episphere distribution of Spectralon diffusing reflection plates under single wavelength.

Fig. 3 illustrates Spectralon diffusing reflections plate in 0 °, 10 °, 30 ° and 45 ° light source incidence zenith angle, 800nm wavelength Under original value (left side) and the hemisphere on the sample surface of ratio Distribution value (right side) on the basis of 30 ° of the optimal zenith angle of detector it is unrestrained Penetrate figure.θ_r=0 °, highest and close to each other at 10 °, is 1.19 times；θ_rThere is minimum at=70 °, be 0.24 times.During due to integration Between different, L_r,refIn θ_i=45 ° of value is less than θ_i=0 °, therefore using proportionality coefficient as standard better than the ratio between original value Compared with.θ_iAt=10 °, figure medium value line it is concavo-convex be due to optical fiber curvature moving or it is manually operated when error cause.

According to Lambert's cosine law (Lambert ' s cosine law), measured value in experiment is corrected.According to Different light source incidence angles, detector zenith angle are grouped as |input paramete, after compared for multinomial, cosine function fitting effect, It was found that cosine function is closer.Spectralon diffusing reflections plate is in different θ when Fig. 4 gives 800nm_iThe cosine function of angle is intended It is distributed after conjunction.Compared to Fig. 3, contour is more smooth, and the correction for algorithm is more accurate.

550nm, the Spectralon diffusing reflection plates episphere point of 715nm are similarly demonstrated according to cosine function relationship formula Cloth.Result shows f (cos θ_r)=Acos θ_rLess, A values are approximately 1.39, B values and are approximately -0.21 the coefficient value changes of+B, this When R²Reach 0.998.So, the average value of 400-994nm is sought as the universal equation of each angle.

Proportionality coefficient and θ under 3 four incidence zenith angles of table_rFunctional relation

Wherein, Y represents proportionality coefficient, and X represents θ_r(Circular measure).

Table 3 analyzes non-ideal optical property of the Spectralon diffusing reflection plates in systematic survey.Experiment shows once The fitting effect of cosine function is optimal, under four incident angles, its R²Value reaches 0.999, and RMSE value is then less than 0.110.A values From 1.33 (θ_i=0 °) change to 1.44 (θ_i=45 °), B values are then from -0.16 (θ_i=45 °) change to -0.24 (θ_i=0°).Due to every Coefficient value is close to each other under individual angle, according to the operating procedure of trimming process, can derive general cosine function formula.By four angles Degree under each measured value see Fig. 4 and Fig. 5 collectively as input, after output A, B value in the middle of numerical value above, R²For 0.9982, RMSE is 0.0134.Finally, θ_i=0 °~45 ° general purpose function expression formulas are：

Y=1.3938cosX-0.2127 （20）

Formula（20）As f (cos θ_r) fitting formula, carry it into formula（16）Can obtain Spectralon diffusing reflection plates Final expression formula it is as follows.

Spectralon diffusing reflections plate is in different θ when Fig. 5 gives 800nm_iThe L after correction under angle_r,refDistribution value Figure, this figure is the result figure of Spectralon diffusing reflection plate bearing calibrations in the present invention.

Claims (9)

1. a kind of Spectralon diffusing reflections plate bearing calibration, it is characterised in that comprise the following steps：

1) light source never irradiates Spectralon diffusing reflection plates with zenith angle, is never adopted with zenith angle and azimuth using spectrometer Collect corresponding reflected spectrum data；

2) spectroscopic data in effective wavelength band is intercepted from the reflected spectrum data, and is averaged, reject difference phase To larger spectroscopic data；

3) residual sum of squares (RSS) Rss is asked to remaining spectroscopic data, determines that most stable of detector receives zenith angle θ_r,degreeValue, And set up any detector and receive zenith angle θ_rWith θ_r,degreeRelational expression；

4) relational expression is substituted into the BRDF expression formulas of Spectralon diffusing reflection plates, Spectralon diffusing reflection plates school is completed Just.

2. Spectralon diffusing reflections plate bearing calibration as claimed in claim 1, it is characterised in that in step 1) in, control The azimuth of light source is 0 °, and it is 0 °, 10 °, 30 ° and 45 ° that zenith angle sets gradually, and is entered at each zenith angle of light source using detector Row is gathered one by one, and, from 0 °~70 ° every 10 ° of collections, azimuth is from 0 °~360 ° every 10 ° of collections for zenith angle.

3. Spectralon diffusing reflections plate bearing calibration as claimed in claim 2, it is characterised in that close light source, control is visited Survey device and corresponding ambient light spectrum data, and the original spectrum that will be gathered under light source are gathered with equal zenith angle and azimuth again Data and ambient light spectrum data do difference treatment, obtain step 1) in reflected spectrum data.

4. Spectralon diffusing reflections plate bearing calibration as claimed in claim 1, it is characterised in that described effective wave band model Enclose is visible ray and near infrared light wave band.

5. Spectralon diffusing reflections plate bearing calibration as claimed in claim 1, it is characterised in that in step 2) in, according to The acquisition interval of detector zenith angle is grouped to spectroscopic data, calculates every group of average value of spectroscopic data, and to spectrum number According to carrying out secondary rejecting treatment.

6. Spectralon diffusing reflections plate bearing calibration as claimed in claim 5, it is characterised in that at described secondary rejecting Manage and be：Spectroscopic data is tentatively rejected using formula (1), remaining spectroscopic data is averaged, recycle formula (2) right Remaining spectroscopic data carries out the treatment of rejecting again；

$|100\&times;\frac{L_{n1}(i,j)-M_{n1}(i,j)}{M_{n1}(i,j)}|<25---\left(1\right)$

$|100\&times;\frac{L_{n2}(i,j)-M_{n2}(i,j)}{M_{n2}(i,j)}|<15---\left(2\right)$

In formula, L, M is respectively original spectral data and corresponding spectroscopic data average value in each group, and n is represented according to detector Zenith angle is grouped value, L_n1、M_n1The average value matrix of original spectral data and spectroscopic data respectively in first time each group, L_n2、 M_n2Original spectral data and the average value matrix of spectroscopic data in respectively second each group, i, j be respectively azimuth value and Wavelength.

7. Spectralon diffusing reflections plate bearing calibration as claimed in claim 6, it is characterised in that described step 3) in ask The formula of residual sum of squares (RSS) Rss is,

$Rss=\sqrt{\frac{\underset{i=1}{\overset{m}{\&Sigma;}}\underset{j=1}{\overset{k}{\&Sigma;}}{\left(\frac{L_{n3}(i,j)-M_{n3}(i,j)}{M_{n3}(i,j)}\right)}^2}{m\&times;k}}$

In formula, L_n3、M_n3Original spectral data and the average value matrix of spectroscopic data after respectively secondary rejecting treatment in each group, i, J is respectively azimuth value and wavelength, m, and k is respectively detector azimuth and wave band number after the secondary rejecting of spectroscopic data.

8. Spectralon diffusing reflections plate bearing calibration as claimed in claim 7, it is characterised in that in step 3) in, with residual The small corresponding collection zenith angle of difference quadratic sum Rss numerical value differences is that the detector of stabilization receives zenith angle.

9. Spectralon diffusing reflections plate bearing calibration as claimed in claim 1, it is characterised in that the Spectralon overflows The step of asking for of the BRDF expression formulas of reflecting plate includes：

4.1st, initial BRDF expression formulas are determined

$f_{r,ref}({\mathrm{\&theta;}}_i,{\mathrm{\&phi;}}_i,{\mathrm{\&theta;}}_r,{\mathrm{\&phi;}}_r,\mathrm{\&lambda;})={\mathrm{\&rho;}}_H\&times;\frac{{\mathrm{dT}}_{ref}({\mathrm{\&theta;}}_i,{\mathrm{\&phi;}}_i,{\mathrm{\&theta;}}_r,{\mathrm{\&phi;}}_r,\mathrm{\&lambda;})/{\mathrm{cos\&theta;}}_r}{\&Integral;{\mathrm{dT}}_{ref}({\mathrm{\&theta;}}_i,{\mathrm{\&phi;}}_i,{\mathrm{\&theta;}}_r,{\mathrm{\&phi;}}_r,\mathrm{\&lambda;}){\mathrm{d\&omega;}}_r}---\left(3\right)$

In formula, θ_iIt is light source zenith angle, φ_iIt is light source azimuth angle, θ_rIt is detector zenith angle, φ_rIt is detector azimuth, λ tables Oscillography is long, d ω_rIt is reflected radiation solid angle, ρ_HIt is the DHRF of Spectralon diffusing reflection plates, dT_refIt is detector in any day Value under drift angle；

4.2nd, the correction set up between the collection spectroscopic data of most stable zenith angle and the collection spectroscopic data of any zenith angle is closed It is formula,

dT_ref(θ_i,φ_i,θ_r,φ_r, λ) and=dT_c,ref(θ_i,φ_i,c,φ_r,λ)·f(cosθ_r) (4)

4.3rd, formula (4) is substituted into initial BRDF expression formulas (3), the Spectralon diffusing reflection plates being calculated after correction BRDF expression formulas.