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GAO Visible to Infrared Imaging Spectrometer

Calibration and Validation

Report 2020

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Spatial Calibration, Radiometric Calibration, Flight Validation, and Wavelength ValidationDavid E. Knapp, Joseph Heckler, Megs Seely, Gregory P. Asner

Last updated 4/2/2020

Overview

This document reports the procedure and results from the spatial calibration, radiometric calibration, and spectral wavelength validation exercises in preparation of the GAO-3 VSWIR imaging spectrometer for the 2020 flight season.

• The spatial calibration process characterizes the spatial response of each detector pixel to a uniform light source as it moves across the field of view of the instrument.

• The radiometric calibration process characterizes the response of each detector to a source of known radiance.

• The wavelength validation process validates the calculated wavelength centers.

Imaging Spectrometer Characteristics The GAO primary instrument is an on-board imaging spectrometer, the GAO Visible to Shortwave-Infrared Imaging Spectrometer (GAO-VSWIR). Below are characteristics:

Characteristic GAO-VSWIRWavelengthRange 350-2500nmSpectralResolution 5nmSpatialResolution 0.5-2.0mSampling 14-bitFieldofView 34˚IFOV 1.0mrad

The GAO imaging spectrometer is a pushbroom array that must be calibrated properly to ensure signal uniformity across the array.

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Equipment and Supplies

The GAO imaging spectrometer calibration procedures require the following equipment to perform the above calibration measurements:

Figure 1. Labsphere integrating sphere with tungsten halogen light sources and peripherals.

1) Labsphere (North Sutton, NH, www.labsphere.com) integrating sphere with 8” viewport and high-intensity tungsten halogen light sources, each modified with KG-2 filters at sphere input apertures.

Figure 2. Spectral validation sources: pen laser with custom diffuser (2a) and helium lamp with custom diffuser (2b).

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2) Helium gas lamp with diffuser.

Figure 3. Mount for NIST-lamp and Spectralon panel.

3) Standard of known radiance. a. Optronic Labs (Orlando, FL, www.ghinstruments.com/) NIST-calibrated

standard of spectral irradiance (tungsten coiled lamp) b. Flat Spectralon panel c. Lamp power supply d. Mounting apparatus

4) Tools and supplies.

a. Small flat-head screwdriver b. Methanol and cleaning wipes c. Compressed dry nitrogen (to clean the integrating sphere as needed)

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Collecting measurements for spatial calibration

The spatial calibration process characterizes the spatial response of each detector pixel to a uniform light source as it moves across the field of view of the instrument. This flat field correction technique ensures that illumination of the GAO imaging spectrometer by a uniform signal will produce uniform output.

When converting raw DN to spectral radiance, an ideal model will require offsets to achieve matching zeroes and a gain scalar to account for responsivity and throughput. In a push broom array sensor system like the GAO-VSWIR, there is a 2D array of detectors, a wide field of view, and optics. This results in a disparity in terms of total responsivity in both the sample and the band directions. The goal of the spatial calibration is to correct for variation with a 2D array of responsivity-leveling gain factors: a flat field array.

Ideally, one could simply point the sensor at a uniform source, apply offset corrections, and use the reciprocal of a mean focal plane array as a flat field. However, it is rarely this easy since the instrument has a wide field of view and it is difficult to create a large and angularly independent radiance source. The solution is to translate an integrating sphere across the field of view of the sensor. Then, build a pseudo-cube by carefully determining which columns of which frames capture the central portions of the sphere aperture. This creates a virtual sphere aperture that spans the full field of view of the sensor by carefully combining the frames where the sensor was observing the central portion of the sphere.

Figure 4. Illumination of the GAO-VSWIR imaging spectrometer with the integrating sphere.

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In this procedure, the integrating sphere is slowly translated back and forth through the instrument field of view perpendicular to the flight direction multiple times creating the output shown in Figure 5.

Figure 5. 640 x 9760 single band mean of dark-subtracted sphere image.

Collecting measurements for radiometric calibration

The radiometric calibration process characterizes the response of each detector element to a source of known radiance. This target of known radiance is a NIST-traceable tungsten halogen lamp that emits a known spectral irradiance valid at 50 cm from the lamp when powered by a stable current.

The irradiance values of the lamp were converted to radiance by reflecting the light from the lamp off a Spectralon panel of measured reflectance. The lamp and panel were mounted to an apparatus that holds the lamp at 50 cm distance from the Spectralon panel. This apparatus is placed beneath the imaging spectrometer, which views the panel at a 45˚ viewing angle while recording scenes with the apparatus in both the open and closed shutter positions.

After dark subtracting and artifact correcting, the raw imaging spectrometer data calculate the ratio of the mean instrument signal to the calibrated radiance of the lamp/panel and corrects for the Spectralon 45-degree angle BRDF factor. The ratios for each wavelength center form the radiometric calibration coefficients that convert instrument digital-number measurements to at-sensor radiance.

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Collecting measurements for wavelength validation

The wavelength validation process validates the calculated wavelength centers and measures any spectral smile across the focal plane. There are two methods to carry out the wavelength validation: 1) ground-based measurements of a well-known spectral emissions target and 2) comparing modeled to measured atmospheric absorbance features in flight data. A helium lamp source was used resulting in the output shown in Figure 6.

Figure 6. Dark subtracted 640-480 mean focal plane derived from helium lamp source.

Spatial calibration Methods

1. Use the spatial calibration moving-sphere data set as input to find the apparent left and right edges of the sphere aperture, along with the apparent sphere aperture center and width in terms of the 640 raw VSWIR columns. We use this data to build a rather sophisticated pointer array that tells the user which frames for which columns observed a certain fraction of the sphere aperture.

2. Accurately finding the left and right edges of the sphere is critical for the flat fielding process. The first step involves averaging a set of high-signal bands in a dark-frame-subtracted cube to get a single band image of the sliding sphere geometry.

3. The procedures have the following inputs: input file, starting sample, ending sample (the 0-based indices of the live portion of the array in the column direction, currently 16

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and 613), and fraction of sphere to use (the portion of the sphere to allow into the flat field, 1/3 used).

4. It returns the following parameters: left, right (the nl vectors of the derived left and right side of the full sphere aperture), center, width (the apparent center and width of the full sphere aperture as expressed in 0-639 column units), and frame_map_number_of_pixels and frame_map_pointer.

5. The map frame pointer array that tells the user which 0-based frame numbers are associated with the sensor viewing each of the n columns of the central frac portion of the total sphere aperture.

6. The sphere aperture was measured to be approximately 435 GAO-VSWIR columns wide at nadir. The frac parameter limits our measurements to 1/3 of the total sphere aperture, for uniformity, and to subset that 1/3 aperture view into exactly 145 samples (435/3).

7. Moving the sphere across the field of view introduces the extra complexity that the sphere aperture size in VSWIR samples decreases with off-nadir angle. We model this parabolic effect and account for it, adjusting each off-nadir sphere look to be combined accurately into the 88-sample 1/3 of total at-nadir framework.

a. Figure 7 shows the derived left, right, and center vectors.b. Figure 8 shows the derived width as a function of frame number and one can see

the issue imposed by sphere translation.

Figure 7. Left, right and center (R, G, B) locations of the sphere aperture.

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Figure 8. Apparent sphere width in number of GAO-VSWIR samples.

c. The returned map frame pointer array (640,145). Each element of the pointer array points to the 0-based frames where that column of the VSWIR detector (0-639) pointed at the relevant and equivalent-width-adjusted column of the central 1/3 of the sphere aperture (0-145). The number of map frame pointers is a 2D image that stores how many frames point at each width-adjusted central-frame-fraction position for each array sample, and how many are in each pointer array element.

i. Figure 9 shows the image of the 2D histogram data in the number of map frame pointers. Bright diagonals are places where the dragging was slower and thus dwelt longer in certain regions.

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Figure 9. 640 x 145 histogram image of the count of frames falling in each of the width -adjusted central third samples of the sphere aperture. Bright diagonals are places where sphere translation was slower and thus dwelt longer in certain regions.

8. We ran our flat field procedure using an offset-corrected cube (generated from the most recent radiance correction code) and the pointer array from the sphere-finding procedure to extract the relevant spectra and to build the actual flat field array.

a. To build the flat field, use the frame pointer array, the number of frames array, and a dark corrected data cube as inputs to our procedure to build the flat field.

b. We built a 640 * 480 accumulation of all the dark-corrected spectra of the central fraction of the sphere for each array column. The code accumulates the summed spectra then normalizes by the count for each array column.

i. Figure 10 shows the raw accumulated image.ii. Figure 11 shows the count vector.

iii. Figure 12 shows the normalized dark corrected GAO-VSWIR pseudo image used to build the final flat field.

Figure 10. Raw pseudo image summation prior to normalization by count.

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Figure 11. Count of frames used for normalization of Figure 12 by sample number.

c. To build the final flat field gain array, create a single representative spectrum, either mean or median, from the normalized image as shown in Figure 12.

Figure 12. Normalized image of central fraction of sphere aperture.

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Figure 13. Representative spectrum from normalized central fraction image.

d. The final flat field array is calculated by dividing that representative spectrum by every column of the normalized pseudo image so that, when multiplied by the flat field array, every column becomes exactly the representative spectrum and the image is uniform or flat.

e. Calculate a final unit mean to be sure the flat field array imposes no overall gain effect, such that the mean value is 1.00. Figure 14 shows the associated final flat field image. This is the final data product.

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Figure 14. Final flat field unit-mean gain array, shown with a 0.8 to 1.2 stretch.

Radiometric Calibration Methods

Once the data have been zero-offset corrected and made uniform in proportional response by flat fielding, the only remaining unknowns in the calibration are band-by-band scale factors to convert those radiance-proportional raw DN to spectral radiance. This is measured using a calibrated radiance spectrum from an external source measured under exactly the same conditions as the imaging spectrometer measured the [integrating sphere flat field] source.

1. Use the data collected for the radiometric calibration as input for this radiance correction with a set of dummy RCCs in which every RCC is 1.0. This will produce pseudo radiance images in which the values are raw DNs with the various corrections (dark pedestal, etc.) applied.

2. Build the mean focal plane from the 1.0 RCC processed data and place it within a 640x480 array, at 16,16 (0-based).

a. We did this for both the open and closed shutter states and subtract the closed from the open array. This method offsets any ambient or stray light that may be present in the imaging spectrometer field of view.

3. Take the reference radiance curve for the NIST lamp/panel and resample it to the wavelengths of the imaging spectrometer.

4. Take the center 200 pixels of the mean focal plane and build a median spectrum, then ratio that spectrum with the resampled NIST lamp/panel spectrum. The output is a text file with the new RCCs.

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Figure 15. NIST-traceable radiance from the calibration lamp reflecting off Spectralon at 45˚ view angle compared to retrieval by the GAO-VSWIR after deriving new radiometric calibration coefficients (RCCs).

On-the-ground wavelength validation Methods

1. Use the data collected for the on-the-ground wavelength validation as input to: a. Find the mean focal plane array.b. Build a 640*480*number_of_lines dark subtracted float cube.

2. Use the dark-subtracted cube as input to generate dark-subtracted means for the wavelength validation.

3. In this case, we’ll use the known characteristics of helium (NIST He) to compare GAO-VSWIR band centers to helium spectral wavelengths in a vacuum.

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a. As shown in the table below, the differences in spectral feature locations between GAO-VSWIR and reference helium wavelengths are well below one half of the 5nm sensor band spacing.

ReferenceHeliumSpectral

Wavelengths(nm)(vacuum)

VSWIRBandCenter(~5nmbandwidths)

Difference(nm)

447.3 446.8 0.5471.5 471.8 -0.3492.4 491.8 0.6501.7 501.8 -0.1587.8 587.0 0.8668.0 667.1 0.9706.7 707.2 -0.5728.4 727.2 1.21083.4 1082.7 0.71869.1 1868.9 0.22058.8 2059.2 -0.4

Table 1. Comparison of known helium spectral features to GAO-VSWIR 640 x 480 dark subtracted mean image of helium lamp data.

Radiance Calculation The radiance code for GAO has several offset steps: a bad detector mapping process and two gain steps. Offset Corrections The first offset correction is a simple dark frame subtraction using the mean focal plane of the combined before and after calibration files. It was unmodified here. The second dark correction is the dark pedestal shift (DPS). The DPS method implemented for the GAO uses the mean of the unlit first rows of the focal plane as a direct DPS effect measurement.

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The final dark correction is the electronic panel ghost correction. It uses an unmixing approach to undo the crosstalk between the four 160-sample VSWIR array panels. Gain Elements The gain correction is applied to the dark corrected data in two parts: flat field (FF) and radiometric calibration coefficients (RCC). The flat field uses the unit-mean flat field array to correct the total throughput of the sensor for each optical angle and each detector on the 2D array. Finally, the radiometric calibration coefficient curve is applied to convert the dark-corrected and flat-fielded raw DN to units of calibrated spectral radiance. These two steps are performed in a single array multiplication by combining the RCC vector and FF array in the processing of the raw data. Bad Detector Derivation The processing of the raw data to radiance uses the calibration files to attempt to find dynamic bad detectors and mask them. This uses a covariance model to identify the bad elements dynamically from flightline to flightline.

Conclusions The GAO-VSWIR was calibrated for the 2020 flight season, resulting in a new flat field, radiometric calibration coefficients and validation of the spectral wavelengths of the detector array. The spatial calibration ensured uniformity across the detector array. This was validated by the helium lamp wavelength validation process that measured the GAO-VSWIR spectral uniformity with uncertainty of less than +/- 2.5 nm. Routine checks of the spectrometer’s spectral stability indicate that it varies no more than approximately 0.3 nm.