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

Direct Matching

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.

Minimum Flicker

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 subject.

Program Features


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 position.

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.

Stimulus Patterns

The available stimulus patterns depend on the method used. The direct matching stimulus contains two half disks with size radius and separation gap.

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 stimdegree.

Response Keys

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.

Program Parameters

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 cps parameter.

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 of adjustment.

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 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.

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.

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.

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.

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:

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.

A rectangular stimulus field with width and height containing the variable test color. Its comparison is the background field color.

Similar to RECTPATTERN but the test pattern is the string dspmsg written in textfont at textsize.

A periodic pattern of vertical stripes, defined by cpd.

A periodic pattern of horizontal stripes, defined by cpd.

vx , vy , vL (float)
This are the coordinates of the variable comparison stimulus.

Example Experiments

Brightness Equations for Colored Lights

Parameter file lum.x from directory \pxl\app\lum

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Author: Hans Irtel