# Presentation: 175970

## A SYSTEMIC RADIOMETRIC CALIBRATION APPROACH FOR LDCM AND THE LANDSAT ARCHIVE – An Update

- LDCM Science Team Meeting
- June 12-14, 2007
- Oregon State University

- Dennis Helder,  EE & CS Dept, SDSU
- Dave Aaron, Physics Dept, SDSU
- Jim Dewald, SDSU IP Lab
- Tim Ruggles, SDSU IP Lab
- Chunsun Zhang, SDSU GISc Center

## A SYSTEMIC RADIOMETRIC CALIBRATION APPROACH FOR LDCM AND THE LANDSAT ARCHIVE

- Consistent calibration of the Landsat archive through use of pseudo-invariant sites
- Techniques for relative gain calibration/correction of large linear arrays
- Vicarious calibration of LDCM and Landsat TM/ETM+ instruments

## Techniques for relative gain calibration/correction of large linear arrays

- Relative Gain—whiskbroom to pushbroom scanner issue:
- Landsat 4/5 TM—16 detectors/refl. band + 4 thermal det.  100 det.
- Landsat 7 ETM+ -- add the pan band & 30m thermal band  136 detectors
- Advanced Land Imager 320 multispectral detectors/sca x 4 sca’s/band x 9 bands + 960 pan detectors/sca x 4sca’s/band = 15,360 detectors
- LDCM ≥ 57,000 detectors!
***Relative gain estimation is a critical element for LDCM!***
- Methods to estimate Relative Gain
- Image uniform fields
**Statistical based methods**
**Lifetime data sets**
**Individual scenes**
**90****o**** yaw maneuvers**

## Relative Gain Estimation Techniques

- Lifetime Histogram Statistics Method
- Over ‘long’ periods of time each detector observes the same data statistically.
- Ratios of detector means or standard deviations can be used to estimate relative gains.
- Individual Scene Statistics Method
- Odd/Even detector striping most prevalent due to focal plane design
- Develop an objective function measuring odd/even striping
- Use least squares approach to minimize objective function through estimation optimal relative gains.
- Yaw Data Sets
- ‘Perfect’ 90o yaw maneuver allows each detector to observe same point on the earth’s surface.  Deterministic estimate of relative gain is possible.
- Near 90o yaw maneuver provides very uniform scene for relative gain estimate, but not perfect.
- Use these data sets with statistical algorithms to develop a more accurate estimate of relative gains.

## Theory of New Method

- Adjacent detectors see nearly the same data.
- Difference between adjacent detectors should be small.
- Develop function to minimize difference between adjacent detectors.

## Symbols

- Qij – pixel value at point i, j (row, column).
- Qij – pixel value before relative gain correction (original value).
- rj – relative gain for detector (column) j.
- Qij = rj Qij.
- F(Q,r,i,j) – objective minimization function.

- o

- o

## Setup Minimization Function F(Q,r,i,j)

- 1 Band of 1 SCA of an ALI Scene.

- Minimize difference between columns 1 and 2.

- Square differences to ensure positive numbers.

## F(Q,r,i,j) Cont.

- Or in General

- Expanding the Quadratics

- Express as a Sum of Products

## F(Q,r,i,j) Cont.

- Recall

- Then Substituting

- We now have a minimization function containing each detector relative gain.

- From the above equation, we can see that each      appears in
- and                  .
- So each      appears in exactly 2 equations of the minimization function, except for      and      which only appear in the first and last equations, respectively.

## F(Q,r,i,j) Cont.

- To minimize                 , we differentiate it with respect to   .

- By setting this equal to zero we obtain.

- We have a system of linear equations to solve for    .

## F(Q,r,i,j) Cont.

- Putting

- We can now solve for each     .
- The last row of ones forces the mean of     to be equal to 1.
*m* = the number of columns (detectors) in the image.

- in a matrix.

## Results

## Scene: EO12001059230136_PF1_01  (Antarctica)

**Scene: EO12001059230136_PF1_01  (Antarctica)**
**Band: 1p**
**SCA: 1**

## Remove Bias

**Band 1p**

## Correction Factors Using Image Statistics

**Band 1p**

- Detector Number

- Correction Factors
- (1/Relative Gains)

## Corrected Image

**Band 1p**

## Corrected Image

- 1st 320 Lines

**Band 1p**

**Data Range 263-384**

**Data Range 283-386**

## EO12004262105030_HGS – A YAW IMAGE SCA 1 Band 1p

- An example of a yaw image...
- Yaw angle = 88.3o

## Band 1p Cont.

## EO12004262105030_HGS Rel Gains Applied toEO12001059230136_PF1

-  SCA 1 Band 1p

## Band 1p Cont.

- Even and Odd Detectors normalized by equalizing total means.

**Data Range: 263-384**

**Data Range: 278-381**

## EO12002329141606_SGS SCA 1 Band 1p

- A 2nd example of a yaw image...
- Yaw angle = 88.5o

## Band 1p Cont.

## EO12002329141606_SGS Rel Gains Applied toEO12001059230136_PF1

- SCA 1 Band 1p

## Band 1p Cont.

- Even and Odd Detectors normalized by equalizing total means.

**Data Range: 263-384**

**Data Range: 279-382**

## EO12004262105030_HGS EO12002329141606_SGSSCA 1Comparison

## EO12004262105030_HGS           SCA 1

| Band | 1p | 1 | 2 | 3 | 4 | 4p |
| --- | --- | --- | --- | --- | --- | --- |
| Odd Ang. (deg) | 88.2632 | 87.9966 | 88.8023 | 88.9465 | 88.9465 | 88.9322 |
| Odd Overlap (%) | 0.9385 | 0.9289 | 0.9578 | 0.9629 | 0.9629 | 0.9624 |
| Even Ang. (deg) | 87.9828 | 87.9966 | 88.418 | 88.65 | 88.65 | 88.6034 |
| Even overlap (%) | 0.9284 | 0.9289 | 0.9441 | 0.9524 | 0.9524 | 0.9507 |

| Band | 1p | 1 | 2 | 3 | 4 | 4p |
| --- | --- | --- | --- | --- | --- | --- |
| Odd Ang. (deg) | 88.54839 | 88.98058 | 89.16974 | 89.08163 | 88.9604 | 88.99361 |
| Odd Overlap (%) | 0.9487 | 0.9641 | 0.9708 | 0.9677 | 0.9634 | 0.9646 |
| Even Ang. (deg) | 88.43023 | 88.64094 | 89.10714 | 88.75984 | 88.69835 | 88.54317 |
| Even Overlap (%) | 0.9445 | 0.952 | 0.9686 | 0.9563 | 0.9541 | 0.9485 |

- EO12002329141606_SGS           SCA 1

## Slide 28

## Band 1p SCA 1

- EO12004262105030_HGS
- (upper images corrected by
- 2004 yaw scene-based gains)

- EO12002329141606_SGS
- (lower images corrected by
- 2002 yaw scene-based gains

**Data Range: 278-381**

**Data Range: 283-374 **

**Data Range: 279-382**

**Data Range: 283-373 **

- EO12001059230136_PF1
- (Antarctica)

- EO12004166105103_HGS
- (Africa)

## EO12001227182254_AGS_01SCA 1 MS-1p

- Lifetime Histogram Statistics Correction

- Yaw Image-based Correction

- EO12001227182254_AGS_01SCA 1 MS-1p

## Slide 31

## Summary Points

- Lifetime statistics provide good  information of overall relative gain trends within an array
- Assumes relative gains only vary slowly with time
- May require ‘fine tuning’ to optimize estimates
- Individual scene statistics approach is optimal with regard to visual removal of striping
- Addresses problem of small, short term relative gain drift
- Needs to be adapted to longer duration data sets
- May be excellent for use with yaw images
- Use of imagery collected during 90o yaw maneuvers can provide excellent information on detector gains
- Need to image uniform surfaces
- Should be executed on a regular (monthly to quarterly?) basis
- Can be done with minimal impact to normal imaging by considering polar regions and possibly deserts.