Brightness Equations of Polychromatic Lights
The application lum is used to find pairs of color stimuli that are
equal in brightness according to different criteria. The following criteria
are supported: direct brightness matching, minimally distinct border,
minimum flicker, and minimum apparent motion.
Brightness Equation Methods
Here the stimulus display is a bipartite field with a small gap separating
the standard and the comparison field. The subject has to select the field
which is the brighter one. An adaptive method may be used to find the point
of subjective equality. This method gives results which are valid for static
stimuli under natural viewing conditions. Its major drawback is that the
results generate a brightness scale which is not additive. Furthermore the
direct brightness matching results of short wavelength stimuli are generally
higher than those of the other methods. Thus blue stimuli look brighter in
direct matching conditions than within other (dynamic) conditions.
This is the classic method of luminance comparison. The standard CIE 1924
spectral luminous efficiency function V(L) is based on flicker
photometry. The standard stimulus is a circular patch with the standard and
comparison color being switched around periodically with about 15 Hz. Since
the hue fusion frequency is lower the hues fuse. However, brightness fusion
frequency is higher and thus if the two colors differ in brightness then
there will be visible flicker. The subject's task is to adjust the target
color until the flicker is minimal. This method should be used if an
additive luminance scale is to be generated. Reliable results, however,
require rather large stimuli.
Minimally Distinct Border
This method of Boynton (1968) is
based on the observation that the border between two directly adjacent color
fields looks blurred when there is no luminance contrast between the two
colors. The subject sees two directly adjacent fields and adjusts the target
color intensity until the border between target and comparison is minimally
distinct. Wagner (1972) have
shown that the results of the minimally distinct border method are
equivalent to the minimum flicker method. The stimulus is static
but it must contain a rather sharp border between the two color fields. Some
care has to be taken that the retinal image of the border ist in focus.
Minimum Apparent Motion
The most advanced method of brightness comparison is the minimum apparent
motion technique. The implementation used here is equivalent to the one
described by Cavanagh, and
Anstis (1987). The method uses an apparent motion pattern
where the direction of perceived motion depends on which of the two stimuli
is brighter. If both are equal in brightness then there is only a stationary
flicker without motion.
There are 2 different task available: One shows a pattern with fixed
intensities and the subject has to give the perceived direction of motion,
and the other task allows the subject to adjust one of the stimulus
intensities until the motion disappears. The minimum motion method shows
the same results as flicker photometry but is easier to judge for the
The color stimuli are defined by the parameters ax, ay, aL,
and vx, vy, vL. The latter are the coordinates of the
variable color which is adjusted by the subject or by an adaptive procedure.
If sinusoidal color pattens are used then the stimulus is a mixture of the
two colors with weights which are sinusoidal functions of horizontal
The background field is defined by the usual field color coordinates
fieldcolx, fieldcoly, fieldlum. and the screen colors are
defiend by the respective screen color coordinates.
The available stimulus patterns depend on the method used. The direct
matching stimulus contains two half disks with size radius and
The mimimum motion stimulus always is a horizontal sinusoidal mixture of the
two colors involved. The rectangular area is defined by height and
width. The spatial frequency is defined by the cycles per degree
parameter cpd and the parameter
stimdegree. The latter parameter tells the program how many degrees of
visual angle correspond to the stimulus width. This depends on
observation distance. The dynamic properties are defined by cps which
gives the number of cycles per second.
The minimally distinct border stimulus has as its standard display pattern 2
half disks without a gap in between. The disk size is defined by radius.
The same holds true for the standard stimulus of the minimum flicker method.
Both methods have additional patterns. The pattern RECTPATTERN is a
single rectangular field defined by width and height. In this case the
comparison color is not shown and adjustment should be relative to the field
background color defined by fieldcolx, fieldcoly, and
fieldlum. The same holds for the pattern STRINGPATTERN. This is
the text string dspmsg with font textfont and textsize.
The patterns HSTRIPEPATTERN and VSTRIPEPATTERN are horizontal or
vertical stripes of the test and comparison color. The stimulus rectangle is
defined by width and height and its spatial period by cpd and
The response types used require 3 different keys: The
yeskey and nokey are used
for binary choices or up/down adjustments and the stopkey is necessary
for adjustment procedures to signal the final value. With mouse buttons or
with other response switches the left and right buttons are for choice and
adjustment and the center button is the stop key. For resons of speed the
keyboard cannot be used for adjustment procedures. If there is only a 2
button mouse available then the stopkey may be defined to be a double
button press of both.
- ax , ay , aL (float)
- Each trial is a comparison of two
stimuli. These are the xyL-coordinates of the constant standard stimulus.
The variable comparison stumulus coordinates are given by
vx, vy, and vL.
- cpd (float)
- Number of cycles per degree visual angle for periodic stimulus
patterns. We assume that the stimulus field size is
stimdegree degrees of visual angle.
- cps (float)
- Number of cycles per second for those stimuli that
involve flicker or motion.
- flags (string)
- The following flags are available:
- Switch into slow motion mode. This is for test purposes only.
- Use an oval background field instead of a rectangular field.
- Randomize the position of the standard and comparison stimulus.
- framerate (int)
- Vertical refresh rate of the active video mode. This is an
output parameter only. It may be used to select proper values for the
- gap (int)
- Width of the gap between the two parts
of the direct matching stimuli.
- height , width (int)
- Height and width of rectangular stimulus fields.
- keydelay (int)
- Delay time in milliseconds between successive
changes of adjustable stimuli. This variable may be used to slow down the
rate of change on fast machines, since it might be too fast for the method
- lumframes (int)
- The number of lumframes defines the range
of luminance adjustment that is available in the minimum motion
method. Since all luminance steps have to be computed in advance and saved
in memory, this parameter is critically related to the amount of memory
available. If lumframes is large, then the subject has a large range of
luminance values for adjusting the variable stimulus. However,
lumframes must not be too large, because then the available memory is
not sufficient for computing the gratings. Since the amount of memory needed
for one grating also depends on the value of cps it is possible that
memory overflow is detected only during run time, if a new value of cps
is requested. So check your parameters before starting data collection.
- lumstep (float)
- A parameter that controls the stepsize for the
method of luminance adjustment. The stepsize is also related to device
resolution and to the gamma function. lumstep is an overall parameter
that may also be used to control the speed of change.
- modulation (float)
- This is the modulation parameter of the minimum apparent
motion stimulus' brightness grating component. It should be set to 0.10 for
minimum motion stimuli. If modulation is set to 0.0, then you get a
pure color flicker stimulus where the flicker is a sine wave grating,
identical to the minimum motion stimulus' color grating component.
- method (int)
- This variable defines the method of brightness
matching used. Available are the following methods:
- DIRECT (0)
- Direct brightness matching. In this case the
stimulus field contains two half disks of size radius, separated by a
gap whose width is defined by gap. This method uses an adaptive
pair comparison procedure to find the point of subjective equality.
- MINCONT (1)
- Minimally distinct border method. The stimulus field
is a horizontally divided disk without a gap between the two fields. This
procedure uses the method of adjustment to find the intensity of the
variable stimulus that minimizes the border distinctness.
- MINFL (2)
- Standard minimum flicker method. The stimulus field
is a circular disk and the color stimuli that have to be equated are
exchanged at a rate of cps cycles per second. This procedure also uses
the method of adjustment to find the variable stimulus intensity that
minimizes the brightness flicker.
- MINMOT (3)
- Minimum motion method with pair comparison
judgements. This is the minimum motion stimulus at a fixed intensity of the
comparison stimulus. The subject has to tell whether movement is to the
right or to the left. The procedure uses an adaptive pair comparison to find
the point of subjective equality.
- VARMINMOT (4)
- Minimum motion method with adjustment. This is a
minimum motion stimulus also, but here we use the method of adjustment to
equate the stimulus brightnesses. The subject can adjust the intensity of
the comparison stimulus until there is no definite motion in any direction
but only a locally stationary flicker.
- radius (int)
- This is the radius of circular stimuli.
- stimpos (int)
- The actual position of the comparison stimulus.
If flag R is set then the position is randomized, otherwise it
is determined from the actual value of stimpos. In any case the data
file values of stimpos give the correct position. If stimpos = 1
then the variable comparison is in the upper half, if it is 0 then the
variable comparison is in the lower half of the stimumus area.
- stimdegree (int)
- This parameter tells the program how to convert the
cpd and stimulus size parameter into physical stimulus size on the
screen. It gives the stimulus size in degree and thus should take the
observation distance into account.
- stimpattern (int)
- The minimum countour and the minimum flicker method allow
various different stimulus patterns to be used:
- STDPATTERN (0)
- This is the method's default pattern. For minimum
flicker this is a circular patch and for minimum contour it is a circular
patch divided into two parts.
- RECTPATTERN (1)
- A rectangular stimulus field with width and
height containing the variable test color. Its comparison is the
background field color.
- STRINGPATTERN (2)
- Similar to RECTPATTERN but the test
pattern is the string dspmsg written in textfont at textsize.
- VSTRIPEPATTERN (3)
- A periodic pattern of vertical stripes, defined
- HSTRIPEPATTERN (4)
- A periodic pattern of horizontal stripes, defined
- vx , vy , vL (float)
- This are the coordinates of the
variable comparison stimulus.
Brightness Equations for Colored Lights
Parameter file lum.x from directory \pxl\app\lum
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