John Dolese

Camera Profiler...

Posted: John Dolese 125 Product: Maple 18

March 24 2016

5 0

CameraProfiler.mw

D700_Profile.xlsx

This Application uses the xrite color checker to obtain Forward and Color Matrices as defined by Adobe.

It compares the camera gamut based on the above matrices to the 1931 Standard Observer using LEDs.

Improved Wave Length to Color ...

Posted: John Dolese 125 Product: Maple 18

December 10 2015

3 3

The CIELAB perceptual model of human vision can be used to predict the color of a wavelength in sRGB. I found the CIEDE2000 corrections to hue, chroma, and lighness were required to get the right values in the blue to violet region. The CIEDE2000 results seem pretty close to what I see looking through a diffraction grating considering I have no way of knowing how my eyes are adapted.

Use the new, faster version. It can run in under 1 minute;

nprocWavelength_Color_CIEDE2000.mw and WtoC_data.xlsx

You will need the data for the color matching functions in the WtoC Excel File. The data directory can now be controlled in the mw file.

Visual Gamut and RGB Color Spaces...

Posted: John Dolese 125 Product: Maple 18

October 04 2015

2 6

 Obtain the tri-stimulus XYZ values from the CIE Color matching functions.

 Show the gamut of maximum chroma for the standard observer model with a D65 Illuminant.

 Approximate the white point of a Planckian source and compare to D65.

 Translate the maximum chroma gamut in xy to Lab (CIE L*a*b*) for perceived gamut (Violet and Magenta come together)

 Map the RGB color cube of fully saturated color into Lab and compare to perceivable colors.

10/6/15 Initial Document

12/28/15 Improve RGB gamut with more data points: Procedures added for RGB to Lab: Wavlength Colors now based on CIEDE2000 model for Lab.

Here is the latest version of this document, the MSL_data must be in a directory set in the mw file;

MSL_data.xlsx Vision_RGB_Gamut.mw

Photon Exposure...

Posted: John Dolese 125 Product: Maple 18

September 26 2014

5 0

This application calculates the number of photons reaching a camera sensor for a given exposure. A blackbody model of the sun is generated. The "Sunny 16" rule for exposure is demonstrated. Calculations are done using units.Photon_Exposure_Array.mw

Photon Exposure

Blackbody Model of the Sun

	Plank Constant
	Boltzman Constant
	Light Speed
	Sun Radius
	Earth Orbit
	Sun Color Temperature
	Transmission Factor

Sun: Spectral Radiant Exitance to Earth: Spectral Irradiance

"M(lambda):=(2*Pi*h*c^(2))/((lambda)^(5))*1/((e)^((h*c)/(lambda*kb*Tsun))-1)*(Rsun/(Re_orb))^(2)*tf_atm:"

=

Photopic Relative Response VP vs λ

=

= $Vector(4, {(1) = ` 471 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})$

(ArrayInterpolation for x,y data VPdata returns y' for new x data lambdaP)

Illuminance in Radiometric and Photometric Units:

E__r := sum(Units:-Standard:-`*`(M(Units:-Standard:-`*`(lambda, Unit('nm'))), Unit('nm')), lambda = 200 .. 4000) =

E__po := Units:-Standard:-`*`(Units:-Standard:-`*`(683.002, Units:-Standard:-`*`(Unit('lm'), Units:-Standard:-`/`(Unit('W')))), sum(Units:-Standard:-`*`(Units:-Standard:-`*`(VP[lambda], M(Units:-Standard:-`*`(lambda, Unit('nm')))), Unit('nm')), lambda = 200 .. 4000)) =

Translation from Illuminance to Luminance for Reflected Light;

Object Reflectance

Object Luminance L__po := proc (R__o) options operator, arrow; R__o*E__po/(Pi*Unit('sr')) end proc: =

Illuminance of a Camera Sensor E_ps applied for time t_expdetermines Luminous Exposure H_p;

Ideal Illuminance is determined by the exposure time t_exp, effective f-number N and to a less extent the angle to the optical axis θ;

•	H Luminous Exposure

•	E_ps Illuminance to the Camera

•	N Effective F-Number

•	t_exp Exposure Time

•	θ Angle to the Optical Axis

E__ps_ideal = Units:-Standard:-`*`(Units:-Standard:-`*`(Units:-Standard:-`*`(Pi, Units:-Standard:-`/`(4)), L__po), Units:-Standard:-`*`(Units:-Standard:-`^`(cos(theta), 4), Units:-Standard:-`/`(Units:-Standard:-`^`(N, 2)))):

The camera meter determines the exposure time t_expto balance the object luminance, reflectance and effective f-number. It does this based on an internal constant k and the camera ISO s.

•	s ISO Gain (Based on saturation at 3 stops above the average scene luminance)

•	k Reflected Light Meter Calibration Constant

for Nikon, Canon and Sekonic

•	c Incident Light Meter Calibration Constant

for Sekonic with flat dome

$N^2/t__exp = `#mrow(mi("\`E__po\`"),mo("⋅"),mi("s"))`/c__m$ (Incident Light Meter)

$Units:-Standard:-`*`(Units:-Standard:-`^`(N, 2), Units:-Standard:-`/`(t__exp)) = Units:-Standard:-`*`(`#mrow(mi("\`L__po\`"),mo("⋅"),mi("s"))`, Units:-Standard:-`/`(k__m)):$ (Reflected Light Meter)

Solve for H in terms of the Camera Meter Constant k and s

Es = Units:-Standard:-`*`(Units:-Standard:-`*`(Units:-Standard:-`*`(Pi, Units:-Standard:-`/`(4)), Lo), Units:-Standard:-`*`(Units:-Standard:-`^`(cos(theta), 4), Units:-Standard:-`/`(Units:-Standard:-`^`(N, 2)))):

H = Units:-Standard:-`*`(Units:-Standard:-`*`(Units:-Standard:-`*`(Units:-Standard:-`*`(Pi, Units:-Standard:-`/`(4)), Lo), Units:-Standard:-`*`(Units:-Standard:-`^`(cos(theta), 4), Units:-Standard:-`/`(Units:-Standard:-`^`(N, 2)))), Units:-Standard:-`*`(Units:-Standard:-`*`(km, Units:-Standard:-`^`(N, 2)), Units:-Standard:-`/`(Units:-Standard:-`*`(Lo, s)))) H = (1/4)*Pi*cos(theta)^4*km/s

H__p := proc (s, theta) options operator, arrow; (1/4)*Pi*k__m*cos(theta)^4/s end proc:

=

Note: Meters are typically set for a scene reflectance 3 stops below 100% or 12.5%.

E__ps := proc (N, R__o, theta) options operator, arrow; (1/4)*Pi*Unit('sr')*R__o*E__po*cos(theta)^4/(Pi*Unit('sr')*N^2) end proc:

=

t__exp_ideal := proc (N, s, R__o) options operator, arrow; H__p(s, theta)/E__ps(N, R__o, theta) end proc:

=

Actual exposure time includes typical lens losses;

	Magnification
	Lens Transmittance
	Lens Flare
	Vignetting

Total Lens Efficiency

=

Replacing Eps with q*Eps we get the "Sunny 16" relation between exposure time and ISO;

t__exp := proc (N, s, R__o) options operator, arrow; H__p(s, theta)/(q*E__ps(N, R__o, theta)) end proc: =

t__exp_alt := proc (N, s, R__o) options operator, arrow; k__m*N^2*Pi/(s*q*R__o*E__po) end proc: =

•	The Number of Photons NP Reaching the Sensor Area A;

•	Circle of confusion for 24x36mm "Full Frame" for 1 arcminute view at twice the diagonal:

A__cc := Units:-Standard:-`*`(Units:-Standard:-`*`(Pi, Units:-Standard:-`^`(Units:-Standard:-`*`(12.6, Unit('`μm`')), 2)), Units:-Standard:-`/`(4)):

•	Sensor Bandwidth Photopic Response VP

•	Exposure Time for Zone 5: Rscene=12.5% , Saturation in Zone 8 Rscene=100%

•	Camera ISO differs from Saturation ISO. Typical Saturation ISO is 2300 when the camera is set to 3200. See DxoMark.

The average number of photons for exposure time based on Reflectance of the scene relative to the metered value:

Zone 5;

NP := proc (s, R__o, theta) options operator, arrow; (1/4)*t__exp(N, s, R__meter)*A__cc*q*R__scene*cos(theta)^4*(sum(VP[lambda]*M(lambda*Unit('nm'))*Unit('nm')*lambda*Unit('nm')/(h*c), lambda = 200 .. 4000))/N^2 end proc:

=

Zone 8; R__meter := Units:-Standard:-`*`(R__scene, Units:-Standard:-`/`(Units:-Standard:-`^`(2, 3))):

NP__sat := proc (s, theta) options operator, arrow; (1/4)*t__exp(N, s, R__meter)*A__cc*q*R__scene*cos(theta)^4*(sum(VP[lambda]*M(lambda*Unit('nm'))*Unit('nm')*lambda*Unit('nm')/(h*c), lambda = 200 .. 4000))/N^2 end proc:

=

Approximate Formula

H__sat := proc (s__sat) options operator, arrow; H__p(s__sat, 0)*E__ps(N, 1, 0)/E__ps(N, 1/8, 0) end proc :

= HFloat(78.53981635)*Units:-Unit(('cd')*('s')/('m')('radius')^2)/s__sat

Average Visible Photon Energy

P__e_ave := Units:-Standard:-`*`(Units:-Standard:-`/`(Units:-Standard:-`+`(850, -350)), sum(Units:-Standard:-`*`(Units:-Standard:-`*`(h, c), Units:-Standard:-`/`(Units:-Standard:-`*`(lambda, Unit('nm')))), lambda = 350 .. 850)): =

NPtyp := proc (s__sat) options operator, arrow; H__sat(s__sat)*A__cc/(683.002*(Unit('lm')/Unit('W'))*P__e_ave) end proc:

=

Download Photon_Exposure_Array.mw

Create DNG Matrices Using Optimization...

Posted: John Dolese 125 Product: Maple 18

September 20 2014

2 0

Obsolete

See my Camera Profiler application instead.

This application creates DNG matrices by optimizing Delta E from a raw photo of x-rites color checker. The color temperature for the photograph is also estimated. Inputs are raw data from RawDigger and generic camera color response from DXO Mark.

	Initialization

XYZoptical to RGB to XYZdata

Sr,g,b is the relative spectral transmittance of the filter array not selectivity for XY or Z of a given color.

Pulling Sr,g,b out of the integral assumes they are scalars. For example Sr attenuates X, Y and Z by the same amount.

Raw Balance is not White Point Adaptation.

The transmission loss of Red and Blue pixels relative to green is compensated by D=inverse(S). The relation to incident chromaticity, xy is unchanged as S.D=1.

(See Bruce Lindbloom; "Spectrum to XYZ" and "RGB/XYZ Matrices" also, Marcel Patek; "Transformation of RGB Primaries")

•	XYZ to RGB

$(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb})) = (Matrix(3, 3, {(1, 1) = XR*Sr, (1, 2) = YR*Sr, (1, 3) = ZR*Sr, (2, 1) = XG*Sg, (2, 2) = YG*Sg, (2, 3) = ZG*Sg, (3, 1) = XB*Sb, (3, 2) = YB*Sb, (3, 3) = ZB*Sb})).(Vector(3, {(1) = X_Tbb, (2) = Y_Tbb, (3) = Z_Tbb}))$

$(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb})) = (Matrix(3, 3, {(1, 1) = Sr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Sg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Sb})).(Matrix(3, 3, {(1, 1) = XR, (1, 2) = YR, (1, 3) = ZR, (2, 1) = XG, (2, 2) = YG, (2, 3) = ZG, (3, 1) = XB, (3, 2) = YB, (3, 3) = ZB})).(Vector(3, {(1) = X_Tbb, (2) = Y_Tbb, (3) = Z_Tbb}))$

$Camera_Neutral = (Matrix(3, 3, {(1, 1) = Sr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Sg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Sb})).(Matrix(3, 3, {(1, 1) = XR, (1, 2) = YR, (1, 3) = ZR, (2, 1) = XG, (2, 2) = YG, (2, 3) = ZG, (3, 1) = XB, (3, 2) = YB, (3, 3) = ZB})).(Vector(3, {(1) = X_wht, (2) = Y_wht, (3) = Z_wht}))$

•	RGB to XYZ (The extra step of adaptation to D50 is included below)

$(Vector(3, {(1) = X_D50, (2) = Y_D50, (3) = Z_D50})) = (Matrix(3, 3, {(1, 1) = XTbbtoXD50, (1, 2) = YTbbtoXD50, (1, 3) = ZTbbtoXD50, (2, 1) = XTbbtoYD50, (2, 2) = YTbbtoYD50, (2, 3) = ZTbbtoYD50, (3, 1) = XTbbtoZD50, (3, 2) = YTbbtoZD50, (3, 3) = ZTbbtoZD50})).(Matrix(3, 3, {(1, 1) = RX*Dr, (1, 2) = GX*Dg, (1, 3) = BX*Db, (2, 1) = RY*Dr, (2, 2) = GY*Dg, (2, 3) = BY*Db, (3, 1) = RZ*Dr, (3, 2) = GZ*Dg, (3, 3) = BZ*Db})).(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb}))$

$(Vector(3, {(1) = X_D50, (2) = Y_D50, (3) = Z_D50})) = (Matrix(3, 3, {(1, 1) = XTbbtoXD50, (1, 2) = YTbbtoXD50, (1, 3) = ZTbbtoXD50, (2, 1) = XTbbtoYD50, (2, 2) = YTbbtoYD50, (2, 3) = ZTbbtoYD50, (3, 1) = XTbbtoZD50, (3, 2) = YTbbtoZD50, (3, 3) = ZTbbtoZD50})).(Matrix(3, 3, {(1, 1) = RX, (1, 2) = GX, (1, 3) = BX, (2, 1) = RY, (2, 2) = GY, (2, 3) = BY, (3, 1) = RZ, (3, 2) = GZ, (3, 3) = BZ})).(Matrix(3, 3, {(1, 1) = Dr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Dg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Db})).(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb}))$

$(Vector(3, {(1) = X_D50, (2) = Y_D50, (3) = Z_D50})) = (Matrix(3, 3, {(1, 1) = RX_D50, (1, 2) = GX_D50, (1, 3) = BX_D50, (2, 1) = RY_D50, (2, 2) = GY_D50, (2, 3) = BY_D50, (3, 1) = RZ_D50, (3, 2) = GZ_D50, (3, 3) = BZ_D50})).(Matrix(3, 3, {(1, 1) = Dr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Dg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Db})).(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb}))$

$(Vector(3, {(1) = X_D50wht, (2) = Y_D50wht, (3) = Z_D50wht})) = (Matrix(3, 3, {(1, 1) = RX_D50, (1, 2) = GX_D50, (1, 3) = BX_D50, (2, 1) = RY_D50, (2, 2) = GY_D50, (2, 3) = BY_D50, (3, 1) = RZ_D50, (3, 2) = GZ_D50, (3, 3) = BZ_D50})).(Matrix(3, 3, {(1, 1) = Dr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Dg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Db})).Camera_Neutral$

	Functions

	Input Data

	Solve for Camera to XYZ D50 and T

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Camera Profiler...

Improved Wave Length to Color ...

Visual Gamut and RGB Color Spaces...

Photon Exposure...

Create DNG Matrices Using Optimization...

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