efg's Computer Lab: Spectra Lab Report

Purpose
The purpose of this program is to display RGB colors as a function of wavelength for visible light (380 to 780 nm). A secondary purpose of this program is to display the emission and absorption spectra of hydrogen. The upper and lower wavelength limits for the spectrum can be interactively specified, and interval marks can be displayed if desired. A spectrum can be printed or saved to a 24-bit color BMP file.

Disclaimer
There is no unique one-to-one mapping between wavelength and RGB values. Color is a wonderful combination of physics and human perception. Please consult a textbook, such as Principles of Color Technology by Billmeyer and Saltzman, for a better understanding of color. In particular, I like the way Billmeyer explains color as the product of three curves, since color requires a light source, an object and an observer. The values shown in this project should only be used as approximate colors, for example, in false color schemes.

Discussion
The WaveLengthToRGB function is based on Dan Bruton's work (www.physics.sfasu.edu/astro/color.html) and is in the file SpectraLibrary.PAS, which is part of the download set:

PROCEDURE WavelengthToRGB(CONST Wavelength:  Nanometers;
                          VAR R,G,B:  BYTE);

  CONST
    Gamma        =   0.80;
    IntensityMax = 255;

  VAR
    Blue   :  DOUBLE;
    factor :  DOUBLE;
    Green  :  DOUBLE;
    Red    :  DOUBLE;

  FUNCTION Adjust(CONST Color, Factor:  DOUBLE):  INTEGER;
  BEGIN
    IF   Color = 0.0
    THEN RESULT := 0     // Don't want 0^x = 1 for x <> 0
    ELSE RESULT := ROUND(IntensityMax * Power(Color * Factor, Gamma))
  END {Adjust};

BEGIN

  CASE TRUNC(Wavelength) OF
    380..439:
      BEGIN
        Red   := -(Wavelength - 440) / (440 - 380);
        Green := 0.0;
        Blue  := 1.0
      END;

    440..489:
      BEGIN
        Red   := 0.0;
        Green := (Wavelength - 440) / (490 - 440);
        Blue  := 1.0
      END;

    490..509:
      BEGIN
        Red   := 0.0;
        Green := 1.0;
        Blue  := -(Wavelength - 510) / (510 - 490)
      END;

    510..579:
      BEGIN
        Red   := (Wavelength - 510) / (580 - 510);
        Green := 1.0;
        Blue  := 0.0
      END;

    580..644:
      BEGIN
        Red   := 1.0;
        Green := -(Wavelength - 645) / (645 - 580);
        Blue  := 0.0
      END;

    645..780:
      BEGIN
        Red   := 1.0;
        Green := 0.0;
        Blue  := 0.0
      END;

    ELSE
      Red   := 0.0;
      Green := 0.0;
      Blue  := 0.0
  END;

  // Let the intensity fall off near the vision limits
  CASE TRUNC(Wavelength) OF
    380..419:  factor := 0.3 + 0.7*(Wavelength - 380) / (420 - 380);
    420..700:  factor := 1.0;
    701..780:  factor := 0.3 + 0.7*(780 - Wavelength) / (780 - 700)
    ELSE       factor := 0.0
  END;

  R := Adjust(Red,   Factor);
  G := Adjust(Green, Factor);
  B := Adjust(Blue,  Factor)
END {WavelengthToRGB};

The product of wavelength and frequency gives the speed of light, c = 2.9979 x 10⁸ m/sec. Given the linear wavelengths (in nanometers) on the Visible Light tabsheet, the frequency values are computed (in TeraHertz). While the wavelengths in the spectrum bitmap are linear, the frequencies are not.

The wavelengths of the Balmer series for n = 3 to 9 are calculated once by the FormCreate method.

Most changes in the user interface result in a call to UpdateImage. If the hydrogen emission/absorption spectrum is to be displayed (see below), a set of flags for each pixel column is set to tell if each column is in the Balmer series. Then each pixel column of the spectrum area is considered. The wavelength associated with each pixel column is calculated based on the upper and lower wavelength limit being displayed. The R, G, B components are calculated for the wavelength associated with the pixel column. Changes are made to the R, G, B assignment depending on the type of spectrum being displayed.

The TChart component was used to display the R, G, B functions of wavelength. This requires quite a bit of setup work in Delphi design mode, but only the single FOR loop in the FormCreate method to create the data points for the graph.

The spectrum is always printed 6 inches wide with a height to match the aspect ratio on the screen. The StretchDIBits Windows API call was used to make sure colors look good on any printer.

The Brightness, Y, shown in the graph on the RGB tab was computed using the formula:

The coefficients in this equation properly compute the luminance for monitors having phosphors that were contemporary at the introduction of NTSC television in 1953. Contemporary CRT phosphors are standardized today with CIE luminance from linear red, green and blue to be:

See Charles Poynton's FAQ about Color and Gamma, section C-9 for more information: http://www.poynton.com/

See how to use a "Rainbow" to color Lyapunov Exponents, which includes a slightly newer SpectraLibrary but requires Delphi 4.

Conclusions
The WaveLengthToRGB function in the SpectraLibrary.PAS unit will be very useful in assigning colors to visible wavelengths of light, or any many applications needing false colors.

Keywords
Visible Light Spectrum, Hydrogen Emission Spectrum, Balmer Series, Hydrogen Absorption Spectrum, WavelengthToRGB function, TChart, Scanline, TRGBTripleArray, Print BMP, StretchDIBits, OnMouseMove, GetRValue, GetGValue, GetBValue


Wavelength[nanometers]	400	450	500	550	600	650	700	750
Frequency[terahertz]	749	666	600	545	500	461	428	400

k	Name	Wavelenth Range
1	Lyman	ultraviolet
2	Balmer	near ultraviolet and visible
3	Paschen	infrared
4	Brackett	infrared
5	Pfund	infrared

Visible Light Spectrum and Hydrogen Emission/Absorption Spectra Linear wavelength values [nm] are shown along the bottom edge; non-linear frequency values [THz] are shown along the top edge