Newton's Prism Experiment and Goethe's Objections

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8. Mapping the rays The upper image shows again the crude color approximation by nonlinear HSB, now with a smaller number of color rays. The lower image shows the content of an array with 1000+1 elements on the screen (right plane), starting approximately at the origin. Each color ray hits an element of this array. The wavelength is written into the array. Gaps are filled by linear interpolation. At position R we have many color rays per length, at position V fewer. In order to distribute the energy correctly across the length, the array content is multiplied by a slope factor. This is calculated by a linear interpolation of the slopes between sV and sR. The content of the array is converted into the color space CIE XYZ, using the common colormatching functions, and then converted to sRGB [10],[21],[22]. Compression is here done by Type C, RGB clipping. The spectrum bar is shown banded. 0.70 0.66 0.62 0.58 0.54 0.50 0.46 0.42 0.38 λ / µ m sV 0 1000 12 V R sR Glass SF15 LBlue 0.3800 LRed 0.7000 nBlue 1.7548 nRed 1.6890 rho1 19.0000 rho2 54.0000 For blue alf1 49.0000 bet1 25.4729 alf2 84.0482 bet2 34.5271 defl 73.0482 disp 15.4286
9. Single ray / Illuminant Equal Energy / Compr. Type C / RGB clipping Illuminant Equal Energy has a flat spectrum. Compression is done by Type C, RGB clipping. The spectrum bars are shown banded and continuous. The table shows linear RGB values, the bars were calculated with gamma encoding for sRGB. RGB clipping does not create balanced distributions of colors. No RGB clipping, no RGB gamma encoding Lam L* a* b* R G B 0.38 0.0 5.5 -9.2 0.3 -0.3 1.8 0.39 0.1 16.9 -25.0 0.9 -0.8 5.5 0.40 0.4 53.0 -51.1 3.0 -2.6 18.5 0.41 1.1 105.2 -85.6 9.1 -8.0 56.5 0.42 3.6 175.9 -134.2 27.4 -24.5 175.7 0.43 10.3 221.0 -171.4 53.9 -49.9 376.9 0.44 17.0 215.6 -177.2 56.7 -56.6 474.6 0.45 23.0 185.5 -168.0 37.6 -46.1 480.4 0.46 29.4 141.2 -152.3 4.6 -25.5 450.9 0.47 36.2 70.2 -121.5 -37.9 8.9 345.1 0.48 44.1 -26.5 -77.8 -78.8 51.5 213.2 0.49 52.7 -134.8 -32.1 -114.2 96.5 115.0 0.50 63.6 -254.0 11.3 -157.2 156.2 56.6 0.51 76.3 -290.7 53.9 -209.6 240.0 16.6 0.52 87.5 -243.4 95.3 -236.0 324.8 -14.9 0.53 94.4 -196.6 122.7 -206.5 371.9 -31.1 0.54 98.2 -155.4 143.9 -136.6 384.8 -40.0 0.55 99.8 -114.3 159.6 -32.9 368.9 -43.2 0.56 99.8 -71.6 166.5 100.8 329.1 -42.3 0.57 98.1 -27.4 166.2 256.4 267.1 -38.1 0.58 94.7 16.6 161.0 416.0 189.7 -31.8 0.59 89.7 57.3 153.1 551.3 108.5 -24.5 0.60 83.5 90.0 142.8 630.4 39.3 -17.5 0.61 76.3 111.3 131.0 631.4 -7.2 -11.8 0.62 68.1 120.1 117.1 556.8 -28.9 -7.6 0.63 58.5 117.6 100.8 427.0 -32.0 -4.7 0.64 48.9 109.4 84.3 301.6 -27.0 -2.7 0.65 39.1 96.7 67.4 192.4 -18.9 -1.5 0.66 29.7 82.0 51.1 112.4 -11.6 -0.8 0.67 20.8 66.9 35.9 59.7 -6.3 -0.4 0.68 13.8 54.7 23.8 32.0 -3.4 -0.2 0.69 7.4 43.1 12.8 15.5 -1.7 -0.1 0.70 3.7 29.5 6.4 7.8 -0.9 -0.1 0.70 0.66 0.62 0.58 0.54 0.50 0.46 0.42 0.38 λ / µ m 13 With RGB clipping, no RGB gamma encoding Lam L* a* b* R G B 0.38 0.7 4.2 -8.2 0.3 0.0 1.8 0.39 2.1 12.9 -22.0 0.9 0.0 5.5 0.40 7.0 34.1 -40.1 3.0 0.0 18.5 0.41 17.3 49.7 -58.4 9.1 0.0 56.5 0.42 32.4 72.4 -85.6 27.4 0.0 175.7 0.43 40.8 83.1 -93.5 53.9 0.0 255.0 0.44 41.1 83.3 -92.9 56.7 0.0 255.0 0.45 38.5 81.8 -97.4 37.6 0.0 255.0 0.46 33.1 79.5 -106.4 4.6 0.0 255.0 0.47 37.3 64.0 -99.5 0.0 8.9 255.0 0.48 52.4 13.7 -64.0 0.0 51.5 213.2 0.49 61.9 -30.4 -17.2 0.0 96.5 115.0 0.50 73.2 -60.1 26.0 0.0 156.2 56.6 0.51 85.9 -81.4 67.1 0.0 240.0 16.6 0.52 87.7 -86.2 83.2 0.0 255.0 0.0 0.53 87.7 -86.2 83.2 0.0 255.0 0.0 0.54 87.7 -86.2 83.2 0.0 255.0 0.0 0.55 87.7 -86.2 83.2 0.0 255.0 0.0 0.56 91.6 -54.9 87.9 100.8 255.0 0.0 0.57 97.1 -21.6 94.5 255.0 255.0 0.0 0.58 89.1 -6.4 88.7 255.0 189.7 0.0 0.59 77.1 19.0 80.4 255.0 108.5 0.0 0.60 63.6 51.7 72.0 255.0 39.3 0.0 0.61 53.2 80.1 67.2 255.0 0.0 0.0 0.62 53.2 80.1 67.2 255.0 0.0 0.0 0.63 53.2 80.1 67.2 255.0 0.0 0.0 0.64 53.2 80.1 67.2 255.0 0.0 0.0 0.65 47.0 72.9 61.2 192.4 0.0 0.0 0.66 36.7 60.9 51.1 112.4 0.0 0.0 0.67 26.7 49.4 39.5 59.7 0.0 0.0 0.68 18.7 40.1 28.7 32.0 0.0 0.0 0.69 11.2 31.5 17.7 15.5 0.0 0.0 0.70 5.9 24.1 9.3 7.8 0.0 0.0
Page 1 and 2: Gernot Hoffmann Newton’s Prism Ex
Page 3 and 4: 1.2 Introduction / About Newton Isa
Page 5 and 6: 1.4 Introduction / Goethe says... S
Page 7 and 8: 3. Calculations for the ray path Th
Page 9 and 10: 5. Ray visualization and a photo We
Page 11: 7. Gamut compression 7.1 Gamut comp
Page 15 and 16: 11. Single Ray / Linear Spectrum /
Page 17 and 18: 13. Multiple ray / Illuminants A, D
Page 19 and 20: 15. Conclusions The Conclusions ref
Page 21 and 22: 17. Reverse problem and inverse app
Page 23: 18.2 References [15] Schott AG Opti

Newton's Prism Experiment and Goethe's Objections

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