METHOD FOR ESTIMATE THE INFLUENCE OF SPECKLE ON THE QUALITY OF A RADIOMETRICAL CALIBRATION OF AN IMAGE Spectrometer

Description

[0001] The invention relates to a method for estimating the influence of speckle on the quality of a radiometric calibration of an imaging spectrometer, in particular an imaging space spectrometer.

[0002] Imaging spectrometers are well-known instruments used to acquire hyperspectral datasets. The data product of an imaging spectrometer consists of a spatial coordinate, a spectral coordinate, and an intensity axis. If the instrument observes different fields of view in a specific temporal sequence, a second spatial coordinate can be obtained. Such imaging spectrometers are regularly used in aircraft or satellites, where they can be employed as remote sensing sensors.

[0003] The central components of an imaging spectrometer typically include a telescope array, an entrance slit, a dispersive element, and a two-dimensional detector with multiple detector pixels. The slit is used to select a spatial image line, which is multispectral due to the superposition of several spectral components and extends in a first spatial direction. The light from this image line is then dispersed in a second spatial direction by the dispersive element, typically perpendicular to the first. The resulting two-dimensional image thus contains spatial and spectral information and can be acquired by the two-dimensional detector. A second spatial coordinate can be sampled by acquiring multiple image lines shifted relative to each other.

[0004] Depending on their application, imaging spectrometers are subject to various influencing factors that necessitate radiometric calibration. For spectrometers used in satellites, these include atmospheric absorption and light scattering. Generally, the optical properties of the components also affect the spectrometer's measurement results.

[0005] In radiometric calibration, a diffuser is positioned in front of the telescope array to scatter light, especially sunlight, homogeneously into the instrument. This allows for the calibration of an intensity axis in a plane of the detector. This process produces speckle, i.e., granular, irregular interference patterns caused by random scattering centers in the diffuser, which are detected by the detector.

[0006] In practice, when considering a radiometric calibration, the crucial factor is the size of the error caused by speckle, or whether this error is small enough for the calibration to be usable.

[0007] The present invention therefore aims to enable a simple and reliable estimation of the influence of speckle on the quality of a radiometric calibration.

[0008] The document is state of the art. " Spectral features on reference diffusers: measurements and analysis", by Courreges-Lacoste et al., from "Proceedings of SPIE - The International Society for Optical Engineering " The document describes the origin of spectral features, as well as the measurement used to reproduce and characterize these properties.

[0009] The document is state of the art. "A novel measurement approach to quantify diffuser induced spectral features", by F. Richter et al. from "Proc. SPIE 10785, Sensors, Systems, and Next-Generation Satellites XXII " This work discloses a technique for characterizing spectral features based on the direct acquisition of monochromatic speckle patterns at the entrance slit. This enables the observation of spectral features below the spectral and spatial resolution of the spectrometer. The spectral features are derived from various observed speckle patterns by accurately mimicking the real spectrometer in the data analysis.

[0010] Furthermore, the document is based on the state of the art. " Sentinel-5: a novel measurement approach to quantify diffuser induced spectral feature" by T. Burn et al. from "SPIE 10562, International Conference on Space Optics 'The document discloses a measurement method for quantifying the spectral features caused by diffusers. The method is based on the acquisition of monochromatic speckle patterns in the slit over a finely sampled wavelength range. The spectral features at the spectrometer detector are evaluated by post-processing, in which the acquired speckle patterns are integrated along the spectral resolution and the detector pixels.

[0011] This problem is solved according to the invention by a method having the features of claim 1. Further developments of the invention can be found in the dependent claims.

[0012] A method according to the invention serves to estimate the influence of speckle on the quality of a radiometric calibration of an imaging spectrometer, wherein the spectrometer comprises a detector with several detector pixels and a dispersive element that causes a dispersion k, wherein light, in particular sunlight, is coupled into the spectrometer through a diffuser (12) for the calibration. The method comprises the step of calculating a numerical contrast value C detector as C Detektor = 1 M where M represents a total degree of freedom for influencing factors that affect the contrast measurable by the detector, wherein M is composed of several individual degrees of freedom comprising an individual degree of freedom M polarization, an individual degree of freedom M spectral, and an individual degree of freedom M pixel, wherein M polarization depends on a polarization of the light entering the spectrometer, wherein M spectral depends on a spectral resolution λ res of the spectrometer and a correlation between spectrally distinct monochromatic intensity distributions, wherein M pixel depends on a single-pixel area A detector and a correlation area A speckle of a speckle, and wherein the computation is performed for an intensity distribution obtained as a superposition of monochromatic intensities describable by monochromatic fields that are circular complex Gaussian variables.

[0013] This provides a method for a simple and reliable assessment of calibration quality. By calculating a numerical contrast value, it is possible to reliably estimate the degree to which an initial contrast value is reduced. From this, it is possible to deduce how speckle affects a calibration, specifically due to the intensity modulation it causes.

[0014] Various physical assumptions regarding sunlight can underlie the calculations. Generally, incident light can be scattered by the diffuser before passing through the optical components of the spectrometer onto the detector, where integration over a specific period can be performed to obtain measurements for the individual detector pixels. Sunlight can be considered spectrally coherent due to the large distance between the sun and the earth and the corresponding small angle of incidence. Temporal coherence, however, is comparatively low. If integration on the detector is performed for several seconds, as can occur during calibration, cross-correlation terms of interfering fields of different wavelengths can disappear. The intensity distribution to which the detector is exposed can therefore be approximated, as intended, as a superposition of monochromatic intensities.Typically, speckle intensities only affect contrast when they sum on an intensity basis in the spectrometer. Otherwise, speckles usually provide no degree of freedom.

[0015] The numerical contrast value may be reduced compared to an ideal contrast value. In principle, the contrast CI for an intensity distribution I measured by a specific number of pixels can be expressed as CI = σ I / are defined where σ I is the standard deviation of I and The mean value of I is given. Under the aforementioned assumption of circular complex Gaussian variables, this initial contrast value CI = 1 for monochromatic polarized light. The calculation methods according to the invention take into account the fact that this initial contrast value is reduced in a real spectrometer.

[0016] Reduced computational effort can be achieved, in particular, if M is determined as the product of the individual degrees of freedom. For example, M = M polarization · M spectral · M pixels. Specifically, this calculation assumes that at least some or all of the individual degrees of freedom describe independent effects.

[0017] According to one embodiment, M polarization can take on a value between 1 and 2. This allows for consideration of the polarization of the light entering the spectrometer.

[0018] Furthermore, it can be provided that the calculation is based on the assumption that the monochromatic fields of spectrally adjacent monochromatic intensity distributions I(λ) and I(λ + Δλ) exhibit a spectral correlation µ spectral (Δλ) and a dispersive correlation µ dispersion (kΔλ) caused by the dispersive element, where λ is a wavelength and Δλ denotes a spectral distance between the intensity distributions. This effectively implements the assumption that the intensity distribution is a superposition of monochromatic intensities.

[0019] It can be provided that an auxiliary variable B is determined as B = λ res / Δλ, where an overall correlation is determined as µ = µ spectral (Δλ) · µ dispersion (kΔλ), and where M spectral is determined as a function of B and µ during the calculation. A degree of freedom belonging to the spectral resolution of the spectrometer can thus be reliably estimated.

[0020] A degree of freedom associated with the single-pixel area and the correlation area of ​​a speckle can be particularly well estimated if, in the calculation, A speckle is determined on the basis of a two-dimensional scattering pattern of the spectrometer, which is convolved with |µ spectral (µλ)| 2< and an autocorrelation function of the detector, in particular of a detector pixel.

[0021] In general, the area ratio D = A detector / A speckle can be determined during the calculation, where M pixels are determined as a function of D. This allows the contribution of a pixel averaging effect to be taken into account.

[0022] Furthermore, the dispersion k of the dispersive element can be taken into account when calculating M pixels. This allows for a more accurate estimation of the associated degrees of freedom.

[0023] The procedure can further include the step of comparing the numerical contrast value with a target value. This allows determination of whether a particular diffuser, in combination with a specific spectrometer, is suitable for calibration, or to what extent speckle caused by the diffuser affects it.

[0024] An exemplary embodiment of the invention will now be explained in more detail with reference to the attached schematic drawings, of which Figure 1 shows a schematic representation of an imaging spectrometer with a control unit; Figure 2 schematically represents some optical components of the imaging spectrometer; and Figure 3 shows a schematic flowchart of a procedure for quantifying the quality of a radiometric calibration of the imaging spectrometer.

[0025] Figure 1 Figure 1 shows a schematic representation of an imaging spectrometer 10. Some optical components of the imaging spectrometer 10 are shown in Figure 2 schematically represented. The spectrometer 10 includes a control unit 11, which is set up and programmed to control the spectrometer 10.

[0026] The spectrometer 10 comprises a telescope arrangement 13, which is shown purely schematically and can be configured in various ways. In particular, it can be a telescope arrangement in the broadest sense, realized by means of suitable mirrors or other optical components. The spectrometer 10 also includes an entrance slit 22, which defines a first spatial coordinate. Furthermore, the spectrometer includes a dispersive element 18, which causes a dispersion k. The light transmitted through the entrance slit 22 is dispersed by the dispersive element 18, generating a spectral coordinate that is mapped onto a second spatial coordinate, which is perpendicular to the first spatial coordinate. The resulting two-dimensional image contains spatial information with respect to the first spatial coordinate and spectral information with respect to the second spatial coordinate.

[0027] The spectrometer 10 further comprises a detector 14 with an array of detector pixels 16, not all of which are labeled for clarity. The generated two-dimensional image is projected onto the detector 14 and can thus be detected by the spectrometer 10. For this purpose, the control unit 11 can appropriately process the corresponding output signals from the detector 14.

[0028] In radiometric calibration, a diffuser 12 is positioned in front of the telescope assembly 13 to couple incident light homogeneously into the spectrometer 10. Due to the scattering caused by the diffuser 12, an interference pattern with speckle 20 forms on the detector 14; for the sake of clarity, not all of these speckles are labeled.

[0029] The influence of speckle on the quality of a radiometric calibration can be estimated using a method described below.

[0030] In a first step S1, a numerical contrast value C detector is used as C Detektor = 1 M The total degree of freedom M is determined, where M represents a total degree of freedom for influencing factors that affect the contrast measurable by detector 14. M is composed of several individual degrees of freedom, including a single degree of freedom Mpolarization, a single degree of freedom Mspectral, and a single degree of freedom Mpixel. Mpolarization depends on the polarization of the light entering the spectrometer (10), Mspectral depends on the spectral resolution λres of the spectrometer 10 and a correlation between spectrally distinct monochromatic intensity distributions, and Mpixel depends on the single-pixel area Adetector of a detector pixel and the correlation area Aspeckle of a speckle. The calculation is performed for an intensity distribution obtained as a superposition of monochromatic intensities describable by monochromatic fields that are circular complex Gaussian variables.As mentioned, the calculation can be performed in control unit 11.

[0031] In a second step S2, the numerical contrast value C of the detector is compared with a target value. The comparison can involve calculating a difference, a quotient, or any other numerical comparison method.

[0032] In step S1, the calculation determines M as the product of the individual degrees of freedom, i.e., M = M polarisation · M spectral · M pixel .

[0033] M polarization takes on a value between 1 and 2, depending on the polarization of the incident light.

[0034] The calculation in step S1 is based on the assumption that the monochromatic fields of spectrally adjacent monochromatic intensity distributions I(λ) and I(λ + Δλ) exhibit a spectral correlation µ spectral (Δλ) and a dispersive correlation µ dispersion (kΔλ) caused by the dispersive element 18, where λ is a wavelength and Δλ denotes a spectral distance between the intensity distributions. An auxiliary variable B is defined as B = λ res / Δλ, and an overall correlation as µ = µ spectral (Δλ) · µ dispersion (kΔλ). M spectral is then calculated as a function of B and µ.

[0035] Furthermore, in step S1, A speckle is determined from a two-dimensional diffraction pattern of spectrometer 10, which is convolved with |µ spectral (Δλ)| 2< and an autocorrelation function of the detector. The diffraction pattern is determined by the shape and size of the system aperture. Additionally, an area ratio D = A detector / A speckle is determined. M pixels are then determined as a function of D. The dispersion k of the dispersive element is also taken into account. This consideration of the dispersion k is achieved through the aforementioned convolution.

Claims

1. Method for estimating the influence of speckle on a quality of a radiometric calibration of an imaging spectrometer (10), wherein the spectrometer (10) comprises a telescope arrangement (13), a detector (14) with a plurality of detector pixels (16) and a dispersive element (18) which causes a dispersion k, and wherein light, in particular sunlight, is coupled into the spectrometer through a diffuser (12) for the calibration, comprising the step: calculating (S1) a numerical contrast value Cdetector as C Detektor = 1 M where M represents a total degree of freedom for influencing variables that affect the contrast that can be measured by the detector (14), where M is composed of several individual degrees of freedom, which comprise an individual degree of freedom Mpolarization, an individual degree of freedom Mspectral and an individual degree of freedom Mpixel, where Mpolarization depends on a polarization of the light entering the spectrometer (10), where Mspectral depends on a spectral resolution λres of the spectrometer (10) and a correlation between spectrally different monochromatic intensity distributions, where MPixel depends on a single area ADetector of a detector pixel and a correlation area ASpeckle of a speckle, and wherein the calculation is performed for an intensity distribution obtained as a superposition of monochromatic intensities describable by monochromatic fields which are circular complex Gaussian variables.

2. Method according to claim 1, wherein in the calculation (S1) M is determined as the product of the individual degrees of freedom.

3. Method according to claim 1 or 2, wherein Mpolarization assumes a value between 1 and 2.

4. Method according to any one of the preceding claims, wherein the calculation (S1) is based on the assumption that the monochromatic fields of spectrally adjacent monochromatic intensity distributions I(λ) and I(λ + Δλ) have a spectral correlation µspectral(Δλ) and a dispersive correlation µdisper-sion(kΔλ) caused by the dispersive element (18), where λ is a wavelength and Δλ denotes a spectral distance between the intensity distributions.

5. Method according to claim 4, wherein an auxiliary variable B is determined as B = λres / Δλ; wherein an overall correlation is determined as µ = µspectral(Δλ) · µdisper-sion(kΔλ); and wherein Mspectral is determined as a function of B and µ when calculating (S1).

6. Method according to claim 4 or 5, wherein in the calculation (S1), ASpeckle is determined using a two-dimensional diffraction image of the spectrometer (10) convolved with |µspectral(Δλ)|2 and an autocorrelation function of the detector (14).

7. Method according to any one of the preceding claims, wherein an area ratio D = Adetector / ASpeckle is determined during the calculation (S1); and wherein Mpixel is determined as a function of D when calculating (S1).

8. Method according to claim 7, wherein the dispersion k of the dispersive element (18) is taken into account when calculating (S1) Mpixel.

9. Method according to any one of the preceding claims, further comprising the step of comparing (S2) the numerical contrast value with a target value.