1 / 34

On the Value of JunoCam’s Marble Movie Images

On the Value of JunoCam’s Marble Movie Images. G.Eichstädt (1) , and C. J. Hansen (2) (1) Independent scholar, Stuttgart, Germany ( ge@junocam.pictures ), (2) Planetary Science Institute, Tucson, Arizona, USA EPSC 2018 Berlin.

rhallenbeck
Download Presentation

On the Value of JunoCam’s Marble Movie Images

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. On the Value of JunoCam’sMarble Movie Images G.Eichstädt (1), and C. J. Hansen (2)(1) Independent scholar, Stuttgart, Germany (ge@junocam.pictures),(2) Planetary Science Institute, Tucson, Arizona, USA EPSC 2018 Berlin

  2. Goal:Geometrical in-flight calibration of JunoCamon the basis ofraw Marble Movie images

  3. The Challenge: For which x is f(x) = 0 ?

  4. Newton-Method

  5. Newton-Method

  6. Newton-Method

  7. Newton-Method

  8. Newton-Method can fail

  9. Newton-Method can fail

  10. Newton-Method can fail

  11. Newton-Method f(xn ) := xn-1 – f'(xn-1 ) -1 f(xn-1 )

  12. Modified Newton-Method f(xn ) := xn-1 – λ f'(xn-1 ) -1 f(xn-1 ) 0 < λ < 1

  13. Modified Newton-Method f(xn ) := xn-1 – λ f'(xn-1 ) -1 f(xn-1 ) 0 < λ < 1

  14. Modified Quasi-Newton-Method f(xn ) := xn-1 – λ [(f(xn-1 + ε) - f(xn-1 - ε) ) / (2ε) ] -1 f(xn-1 ) 0 < λ < 1; ε > 0

  15. Modified Quasi-Newton-Method applied to JunoCam's Marble Movie images For which camera parameters do the centroids of the three color channels align?

  16. Modified Quasi-Newton-Method Rendition Image JNCE_2016198_00C2103_V01, Iteration 00 Input: 4 parameters to be calibrated Output: 4 centroid offsets Example: 1. optical center x, 2. optical center y, 3. rotation period in units of interframe delays, 4. CCD angle offset around optical axis relative to plane normal to spacecraft spin axis. Error := max { red_x, red_y, blue_x, blue_y } (used to select best iteration step) focalLength=1482.5 pixels, K1=-6.0e-8, K2=3.0e-14

  17. Modified Quasi-Newton-Method Image JNCE_2016198_00C2103_V01, Iteration 00 focalLength=1482.5 pixels, K1=-6.0E-8, K2=3.0E-14

  18. Modified Quasi-Newton-Method Image JNCE_2016198_00C2103_V01, Iteration 01 focalLength=1482.5 pixels, K1=-6.0E-8, K2=3.0E-14

  19. Modified Quasi-Newton-Method Image JNCE_2016198_00C2103_V01, Iteration 02 focalLength=1482.5 pixels, K1=-6.0E-8, K2=3.0E-14

  20. Modified Quasi-Newton-Method Image JNCE_2016198_00C2103_V01, Iteration 03 focalLength=1482.5 pixels, K1=-6.0E-8, K2=3.0E-14

  21. Modified Quasi-Newton-Method Image JNCE_2016198_00C2103_V01, Iteration 15 focalLength=1482.5 pixels, K1=-6.0E-8, K2=3.0E-14

  22. Modified Quasi-Newton-Method Retrieve Data Point Image JNCE_2016198_00C2103_V01, Iteration 14

  23. Vary over values of an assumed parameter, and consider two sets of similar raw Marble Movie images Two camera parameters can be estimated by the intersection region of the chart, here K1 and CenterX, on the basis of the assumed values of the other parameters.

  24. Extend variation to 3 common input and to 3 common output parameters (the 4th parameter RotPeriod is assumed to vary between the image sets) retrieve CenterX retrieve CenterY retrieve ZRot vary K1 vary K2 vary ScaleZX (focal length in pixels) based on the first 20 Marble Movie images of product IDs JNCE_201621x_00C37xx_V01, and on the first 19 Marble Movie images of product IDs JNCE_2016202_00C25xx_V01.

  25. Reduce to the means retrieve CenterX retrieve CenterY retrieve ZRot vary K1 vary K2 vary ScaleZX (focal length in pixels)

  26. Infer system of 6 linear equations with 6 variables, and solve it. Result: approximated 6-parameter camera model CenterX = 808.52502 + 2.261150E+008 * (K1 + 6.0E-8) + 3.834000E+012 * (K2 – 3.0E-14) – 0.082339 * (ScaleZX – 1482.5) CenterX = 806.67173 + 2.447403E+009 * (K1 + 6.0E-8) + 1.599861E+015 * (K2 – 3.0E-14) – 0.712903 * (ScaleZX – 1482.5) CenterY = 611.30991 – 9.343140E+008 * (K1 + 6.0E-8) – 8.140500E+013 * (K2 – 3.0E-14) + 0.190489 * (ScaleZX – 1482.5) CenterY = 609.74769 – 7.543189E+008 * (K1 + 6.0E-8) – 4.715984E+014 * (K2 – 3.0E-14) + 0.113622 * (ScaleZX – 1482.5) ZRot = 0.0014241983 + 1.161489E+004 * (K1 + 6.0E-8) + 4.429550E+008 * (K2 – 3.0E-14) – 0.000003381 * (ScaleZX - 1482.5) ZRot = 0.0013391541 + 1.282944E+005 * (K1 + 6.0E-8) + 8.212703E+010 * (K2 – 3.0E-14) – 0.000019282 * (ScaleZX - 1482.5) K1 K2 ScaleZX CenterX CenterY ZRot = - 5.754751200e-008 = 2.733400054e-014 = 1.482290471e+003 = 809.0865952905 = 609.1956288431 = 0.0014522112

  27. Distortion effect of Brownian K1 and K2 in approximated 6-parameter camera model K1 K2 ScaleZX CenterX CenterY ZRot = - 5.754751200e-008 = 2.733400054e-014 = 1.482290471e+003 = 809.0865952905 = 609.1956288431 = 0.0014522112

  28. Radial Brown-Conrady distortion is usually described by a weighted sum of polynomials r2n+1 next-degree polynomial required to adjust for side effects of lower-degree polynomials Polynomials diverge, when extrapolated

  29. Radial Brown-Conrady distortion is actually an infinite power series Multiply all (even) polynomials with the same Gauss function in order to make them convergent. Introduce equivalent and more benign base of „distortion wavelets“. Polynomials diverge, when extrapolated

  30. Calibration approach: Determine Gaussian sigma, after determining Brownian K1, such that modified K2 ≈ 0 Here, the natural logarithm of sigma is used for the parameter to be optimized.

  31. Comparing Brownian (K1, K2) calibration approach with (K1, sigma) „distortion wavelet“

  32. Color channel alignment errors for a fixed chosen rotation period of 80.952 interframe delays (K1,K2) calibration (K1,sigma) calibration CCD location of data sets 11 10 9 8 7 5 4 3 2 1 Raw Marble Movie Images on CCD layout

  33. Color channel alignment errors for rotation period adjusted to data set (K1,K2) calibration (K1,sigma) calibration

  34. Summary and Conclusion • Marble Movie images provide abundant constraints for geometrical JunoCam calibration and testing, even without shape model, ancillary navigation or pointing data. • "Distortion wavelets" provide mutual annihilation of divergent side effects of Brown-Conrady lense distortion polynomials.

More Related