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Abstract

A 120-frame movie, which can be downloaded from specified web sites, allows an observer to see the qualitative form of his or her temporal modulation transfer function. Results collected from two of the authors are presented.
The spatial contrast sensitivity fun ction is a measure of the extent to which each spatial
frequency of a sinusoidal grating is transferred by the visual system (see DeValois and
DeValois 1988). Sensitivity is highest for spatial frequencies close to 5 cycles deg
ÿ1
and
falls off at lower and higher frequencies (Blakemore and Campbell 1969). Campbell
and Robson (1968) publi shed a chart which allows an obse rver to see the qualitative
form of his or her spatial modulation transfer function (MTF). It is a field of vertical
sinusoidal bars whose spatial frequency increases from left to right and whose contrast
in creases from top to bottom. The lower, high-co ntrast part of the field is visibly stripe d,
whereas the upper, low-contrast part appe ars to be spatially uniform. If sensitivity were
the same at all spatial frequencies, then the line separating the visible from the invisible
region would b e horizontal. In fact, however, the line is bowed upwards at sp atial
frequencies aroun d 5 cycles deg
ÿ1
, showing the lowest threshold (highest sensitivity) at
this frequency. The line slopes downward for lower and h igher frequencies, delineating
the fall off in sensitivity for coarser and finer stripes.
The temporal contrast sensitivity function is a measure of the extent to which each
temporal flicker rate of a spatial uniform field is transferred by the visual system. For
the light-adapted eye, sensitivity is generally highest at temporal frequencies in the
range 5 ^ 10 Hz and falls off at lower and higher temporal frequencies (de Lange 1952;
Kelly 1961; Snowden et al 1995).
We have devised a movie which allows an observer to see the qu alitative form of
hi s or her temporal MTF. This movie, which is the temporal analog of Campbell and
Robson's spatial chart, consists of an array of small, sinusoidally flickering square tiles,
and resembles a graph in which x temporal frequency and y contrast. One frame
of the stimulus is shown in figure 1, and the time sequence is shown schematically
in figure 2. In each successive colum n from left to right of figure 1 the flicker rate
in creases in approximately half-octave steps. In the bottom row of tiles the contrast
is high, and decreases in each successive higher square. The whole tiled area app e ar s
to be divided into a lower, h igh-contrast region in which the flicker is visible and
an upper, low-contrast region which appears to be static, since the flicker is too fast
or too low in contrast to be resolved. If sensitivity were the same at all temporal
frequencies, then the line separating the visible fro m the invisible regi on would be
horizontal. I n fact, however, the line is bowed upwards at temporal frequencies around
5 ^ 10 Hz, showing the lowest threshold ( highest sensitivity) at these frequencies. The
line slopes downward for lower and higher temporal frequencies, indicating the fall off
in sensitivity to higher and lower flicker rates.
Demonstrating the temporal modulation transfer function
P ercep tion, 1999, volume 28, pa ges 623 ^ 626
Stuart Anstis, Leonid Kontsevichô, Christopher Tylerô
Department of Psychology, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0109, USA;
e-mail: sanstis@ucsd.edu Smith Kettlewell Institute of Visual Science, 2318 Fillmore Street,
San Francisco, CA 94115, USA; e-mail: cwt@skivs.ski.org)
Received 30 March 1998, in revised form 10 August 1998
Abstract. A 120-frame movie, which can be downloaded from specified web sites, allows an
observer to see the qualitative form of his or her temporal modulation transfer function. Results
collected from two of the authors are prese nted.
DOI:10.1068/p2766
1
10
100
0.25 0.5 1 2 4 8 1 6
Temporal frequency=Hz
Contrast=%
Figu re 1. Snapshot of the stimulus. Temporal frequency increases to the right and contrast increases
downwards. The screen was divided into 14612 coarse pixels, and e ach pixel varied sinusoidally
over time. All pixels within a column flickered at the same frequency, but with randomized p hases.
Flicker threshold will lie perhaps halfway up e ach column: the exact height depends crucially upon
the temporal frequency.
Contrast
low
medium
high
f 2f 4f
Temporal frequency=Hz
Time
Figure 2. The time course of some sample pixels
from figure 1 is shown; flicker is depicted as square
wave for simplicity, but was actually sinusoidal.
624 S Anstis, L Kontsevich, C Tyler
The stimulus was implemented as a 120-frame movie in Matlab 5.0 on the Macintosh,
and can be downloaded from either of these web sites:
http://www-psy.ucsd.edu/ sanstis/TMTF.html
http://www.ski.org/CWTyler
lab/CWTyler/T MTFDemo/TMTFDemo.html
The file is also available on the Perception web site:
http://www.perceptionweb.com/p erc0599/anstis.html
and will be archived on the Perception annual web site CDRom.
The Matlab source code, written by Chien Chung-Chen, can also be downloaded
from these pages.
When the program is run, the movie runs for 60 s. There are fourteen tempo ral
frequencies ranging from 0.25 to 16 Hz and twelve levels of Michelson contrast ranging
from 0.01 to 1.0 (depending on the monitor settings).
The pic ture size is limited to 6 cm w ide65 cm h igh; to make the picture bigger would
require re-writing the program in some faster format su ch as C or assembly l anguage.
We have prepared two versions of the stimulus. In the first version all the tiles with in a
column (all flickering at the same frequency) were in phase. Th i s generated undesirable
spatiotemporal beat frequencies in the fo rm of vertical lines several columns wide
0.01
0.1 0
1.00
Contrast sensitivity
124 81632
Temporal frequency=Hz
0
ÿ1
ÿ2
ÿ3
LLK
(a)
0.01
0.1 0
1.00
Contrast threshold
110100
Temp oral frequency=Hz
CWT
110100
Temporal frequency=Hz
3
2
1
0
Relative sensitivity
(b)
Ratio of peripheral to foveal sensitivity
Figu re 3. Results from two trained subjects (mean of three tri als). (a) Darkening the stimulus with
neutral density filters moved the MTF curves down and to the left, showing the increasing slug-
gishness of the dark-adapted visual system. Observer: LLK. (b) Peripheral viewing of the flickering
stimulus degrade d sensitivity to low temporal frequencies but enhanced it for high frequencies.
Observer: CWT.
Demonstr ating the temporal modulation tr ansfer function 625
which oscillated horizontally back and forth and changed in width rhythmically as they
did so. We removed these beats by randomizing the phase of each square tile. As a result
the spatial array at any given time was a dense array of grey tiles of random luminance
levels.
Figure 3 shows the results, which were collected from two of the authors. The observer
viewed the monitor screen fro m a distance of 57 c m and drew a continuous line with
a felt-tipped pen on a piece of transparent acetate which was t aped to the screen.
This line divided the scree n into a lower region in which flicker was visible and an
upper regio n in which no flicker was visible. This line defined th e observer's temporal
MTF. The coordinates of the line were encoded later by the exp e rimenter.
Figure 3a shows the effects of dark adaptation: Viewing the stimulus through neutral
density filters of 1.0 or 2.0 log units moved the MTF curves down and to the left,
showing the increasing sluggishness of the dark-adapted visual system. Figure 3b shows
the effects of peripheral viewing. When the observer fixated on a point located 4 deg
above the center of the flickering pattern, h i s sensitivity to low temporal fre quencies
was reduced but his sensitivity to high temporal frequen cies was improved.
Drawing each MTF line took a trained observer only about 10 s, suggesting that this
technique might be suitable fo r teaching a student laboratory class. Analyzing the data
by scanning them into the computer and passing them sequentially through Photoshop,
Macdraw Pro, DataThief, and Excel took longer.
Refer ences
Blakemore C B, Campbell F W, 1969 ``On the existence of neurones in the visual system s electively
sensitive to the orientation and size of retinal images'' Jo urnal of Physiology (London) 203
23 7 ^ 260
Campbell F W, Robson J G, 1968 ``Application of Four ier analysis to the visibility of gratings''
Journal of Physiology (London) 197 551^566
DeValois R L, DeValois K K, 1988 Spatial Vision (New York: Oxford University Press)
Kelly D H, 1961 ``Visual responses to time-dependent stimuli, I. Amplitude sens itivity measure-
ments'' Journal of the Optical Society of America 51 422 ^ 429
Lange H de, 1952 ``Exp eri ments on flicker and som e calculations on an electrical analogue of
the foveal systems'' Physica 18 935 ^ 950
Snowden R J, Hess R F, Waugh S J, 1995 ``The processing of temporal modulation at different
levels of retinal illuminance'' Vision Research 35 775 ^ 789
ß 1 999 a Pion publication
626 S Anstis, L Kontsevich, C Tyler
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  • R L Devalois
  • K Devalois
DeValois R L, DeValois K K, 1988 Spatial Vision (New York: Oxford University Press)