Science and Engineering
Spectra   Lab Report
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
ScreenSpectraGraph.jpg (53402 bytes)

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.

Materials and Equipment

Software Requirements
Windows 95/98/2000
Delphi 3/4/5 (to recompile); need "Professional" version for TChart component

Hardware Requirements
Best when run with a high color or true color display (but will work with only a 256-color display).

Procedure

  1. Set your display adapter to high color (15/16-bit) or true color (24/32-bit), if possible.
  2. Double click on the Spectra.EXE icon to start the program. Just point at any spot in the spectrum to see its R,G,B value.
  3. Use the Low or High SpinBoxes to change the lower or upper bounds of the wavelength range.
  4. Remove interval marks by unchecking the Interval CheckBox. With the Interval CheckBox checked, change the desired interval marks by using the SpinBox.
  5. Check or uncheck the Photo Plate Order CheckBox to change the display order.
  6. Make a selection from the Spectrum RadioGroup to change which spectrum is displayed.
  7. Select the color at any point in the spectrum bitmap by pointing at it with the mouse cursor.
  8. Display a screen of only the selected color by pressing on the small colored square at the lower right.
  9. Print or Save the displayed spectrum by pressing on the Print or Save BMP buttons.
  10. Use the mouse cursor to point at any position on the spectrum bitmap.  Create a "color box" for a specified wavelength by pressing on the Color Box button:

 
Wavelength[nanometers] 400 450 500 550 600 650 700 750 
Frequency[terahertz] 749 666 600 545 500 461 428 400
  1. Select the RGB Graph TabSheet to see Dan Bruton's approximations to R, G and B as a function of wavelength. Select the Intensity or Y (inYIQ coordinates) to display the corresponding intensity of a pixel of a given wavelength. Print the TChart graph, if desired.  (See graph above)
  2. Select the Info about Atomic Spectra for Hydrogen Tabsheet for information about the emission and absorption spectra of hydrogen.

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.

The Balmer emission spectra for hydrogen is computed from this formula:

BalmerSeries.gif (1326 bytes)

where n = 3, 4, 5, ...

The general hydrogen emission series can be computed from this formula:

HydrogenSeries.gif (1326 bytes)

where

RH = Rydberg Constant for Hydrogen = 10,967,757.6 m-1.

n=k+1, k+2, k+3, ...

and k is defined in the following table:

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

For additional details of the hydrogen spectra (and other atoms and molecules) see a good physics book, such as Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd edition) or Quantum Chemistry (5th edition).

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.

Hydrogen Absorption Spectrum (Balmer Series)

HydrogenAbsorptionSpectrum.jpg (6044 bytes)

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:

    Y = 0.299R + 0.587G + 0.114B

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:

    Y = 0.212671R + 0.715160G + 0.072169B

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

See Paul Bourke's Spectrum image:
http://astronomy.swin.edu.au/~pbourke/colour/images/wavelength.jpeg 

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

For information about Color Science, see efg's Color Reference Library pages.

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

References
Dan Bruton's Color Science page,  www.physics.sfasu.edu/astro/color.html

Rendering Spectra, http://mintaka.sdsu.edu/GF/explain/optics/rendering.html 

John Walker's Colour Rendering of Spectra, www.fourmilab.ch/documents/specrend
Mitchell N Charity's comments about this article

Don KlipStein's Spectrawww.misty.com/~don/spectra.html

Download
Delphi 3/4/5 Source and EXE (236 KB): Spectra.ZIP

Delphi 3 EXE: 435 KB
Delphi 4 EXE: 543 KB
Delphi 5 EXE: 578 KB


Updated 31 Jul 2006


since 1 Nov 98