Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A 1767
Effect of luminance on photopic visual acuity in the presenceof laser speckle
Jos6 M. Artigas and Adelina Felipe
Departamento de Optica, Facultad de Fisica, Universitat de Valncia, 46100-Burjassot (Valencia), Spain
Received October 28, 1985; accepted May 16, 1988
Visual acuity in coherent and incoherent light has been determined by using square-wave gratings of 100% contrast.Luminance was varied from 3 to 400 cd/M2 . Coherent illumination resulted in a 40% loss of visual acuity. This isprobably due to the masking effect of coherent spatial noise (speckle). However, the most interesting finding is thechange in shape of the photopic visual-acuity-luminance function. With coherent illumination, the function isvertically displaced and of a different gradient. An increase in luminance produces a decrease in visual acuity.This indicates that the masking effect of the speckle is dependent on luminance. Two observers were used, andsimilar results were obtained by both.
INTRODUCTION
The laser has become ubiquitous as a lighting source foroptical systems. In many cases a human observer is thedetector or the final stage of such a system. The eye pro-cesses the coherent images and provides the output. Someauthors",2 have pointed out that it is impossible to discussthe overall performance, or the quality of the images, with-out knowledge of the performance of the human visual sys-tem.
The speckle found in the image is the main obstacle to theuse of coherent light, and methods have been developed toeliminate or reduce it.3 In recent years, April and Arsen-ault4 have studied this masking effect of speckle in opticalsystems, and Marron and Morris5 have worked on tech-niques for performing image recognition on speckled images.Knowing how images are processed by the observer shouldimprove the performance and design of image-transmissiondevices.6-8
Spatial information processing in the visual system hasbeen studied by determining either visual acuity9 or themodulation transfer function.l0 -'3 Also, sinusoidal andspeckle patterns generated on the retina have been powerfulresearch tools in many studies. These are some data on theeffects of coherence.14-"7 However, a direct comparison hasnot been made between visual processing of images pro-duced by coherent and incoherent light.
Recent experiments by Williams16 show that coherentspatial noise (speckle) can produce potent masking effects,reducing the contrast sensitivity.
We have studied the performance of the dioptrics of theeye with coherent light.15 We determined the effect of co-herence on visual acuity for different pupil sizes. With aconstant luminance of 100 cd/M2 and a 3-mm pupil, wefound that the acuity limit is 28 cycles/degree (c/deg) forcoherent illumination and 43 c/deg for incoherent illumina-tion.
Luminance changes are common in optical systems. Inthis study we examine their effect on visual acuity, with bothcoherent and incoherent light.
METHOD
ApparatusThe light source was a He-Ne Spectra-Physics laser with 25-mW power, a wavelength X = 632.8 nm, and 9.25-cm coher-ence length. The beam passed through a spatial filter andwas collimated by lens L1. One polarizer was used to regu-late the luminance as the laser was itself polarized. Lens L2focused the beam, which acted as a point source to projectthe target onto the screen. A diaphragm limited the obser-vation angle, which was 10 (see Fig. 1).
The observer was seated 1 m from the diffusing glassscreen; his or her head was positioned by a chin-and-fore-head rest. An artificial pupil of 3-mm diameter was placedin front of the natural pupil, which always exceeded 3 mm.A shutter controlled the duration of the observation interval(3 sec). The target was a variable square-wave grating of100% contrast.
A motor rotated the screen to reduce spatial coherenceand consequently the speckle pattern.3"18 From the statisti-cal properties of the reduced speckle pattern, the value ofthe autocorrelation function at zero lag is unity for thespeckle pattern (when the diffuser is held stationary) andfalls to -0.055 for the reduced speckle pattern (when thediffuser moves). That is, the speckle becomes impercepti-ble.
Figures 2 and 3 show the screen under these two condi-tions. The figures were produced by a photographic tech-nique but show the effect of a change in coherence.
ProcedureFive photopic luminance levels were used: 3, 11, 45, 100,and 400 cd/M2 . Luminance was measured by a TektronixJ16 photometer with a 15603 luminance probe, directly pro-ducing the value of luminance in candellas per square meter.
Five sessions were performed at each of these levels. Ini-tially, we found a low, and a high, spatial frequency at whichthe grating was never perceived, and always perceived.Thereafter the range was adjusted so that the probability ofseeing the target could be estimated.
1768 J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988
Po L2 0
m
Fig. 1. The experimental setup used for these experiments. M,mirror; SF, spatial filter: L1, L 2, lenses; P0 , polarizer; So, focal point;0, object; D, diaphragm; S, screen, m, motor; E, shutter; Pu, artificialpupil; Obs., observer.
Fig. 2. Features of the grating observed when the diffuser screen isheld stationary.
Fig. 3. Features of the grating observed when the diffuser screen isbeing rotated.
In each trial, the grating was shown to the observer for 3sec. Between trials, the orientation of the grating was var-ied randomly to one of four orientations: vertical, horizon-tal, 450 right, and 450 left. The observer indicated the ori-entation of the grating and did not guess if he or she wasunable to distinguish the grating. On only 2% of occasions didthe observer incorrectly identify the orientation of the grating.
There were two observers, one male, 30 years of age(JMA), and one female, 31 years of age (AF). Both hadcorrected visual acuities of 20/20 or better. The observersadapted to the luminance of the screen for 5 min at thebeginning of each session.
In addition, visual function with coherent and incoherentlight was compared in the absence of speckle. At low lumi-nance level the high spatial frequency of speckle is invisible.The absolute luminance threshold for the target configura-tion was determined under both conditions. It was foundthat a short learning period was required to produce consis-tent results in the presence of speckle.
RESULTS
Figure 4 shows the results for the two subjects. The per-centage of exposures in which the orientation of the grating
io00 ___COHERENTINCOHERENT
Obs JMA
50- -'
@~~~~~~~~ \ \ b
lo \ 20 o '40 'S~0.U) spatial frequency (c/deg)
4)
i-. 100 -_INCOHERENTo|w Ob, A
no
0
0O 20 30 40 50spatial frequency (c /deg)
Fig. 4. The correct percentage, as a function of the spatial frequen-cies (in cycles/degree), of the grating presented to the observer isrepresented for each of the two observers. Curves 1, 2, 3, 4, and 5correspond to luminance levels of 3, 11, 45, 100, and 400 cd/M2 ,respectively. Results with coherent illumination (dashed lines) andwith incoherent illumination (solid lines) are shown. Each point isbased on 100 observations. Pupil size, 3 mm; X = 632.8 nm.
J. M. Artigas and A. Felipe
J. M. Artigas and A. Felipe ~~~~~~~Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A 1769
Fig. 5. Experimental values of visual acuity (+1c/deg) as afunction of the luminance with incoherent (solid lines) and coherent (dashed lines)illumination for each of the two observers. Pupil size, 3 mm; X= 632.8 nm.
could be identified is plotted against spatial frequency forboth coherent and incoherent illumination. Each plot rep-resents a different luminance level. At each luminance, 60%is taken as the threshold visual acuity. An extra luminancelevel (45 cd/in 2
) was used under the coherent condition.The absolute luminance threshold was identical for coher-
ent and incoherent light.At all luminance levels visual acuity is worse with coherent
lighting when speckle is present. This is summarized in Fig.5. A further difference between the two conditions isshown. The incoherent visual acuity improves slightly withincreasing luminance. This is well known from the classicalliterature. 9 However, in coherent light there is a slow butsteady decrease in visual acuity with increasing luminance ofthe target grating. This is surprising. It has not been ob-served for any other target configuration, as far as we know.
DISCUSSION
The results show that visual acuity is worse with coherentillumination than with incoherent, confirming the results ofour previous work.' 5 The threshold luminance for light isindependent of coherence, and therefore there is no intrinsicdifference in photoreceptor sensitivity. Therefore the de-cline in visual acuity is probably due to the masking' 9' 20
effects of speckle in coherent light.In incoherent light, acuity increased only slightly as lumi-
nance increased (see Fig. 5). The slight increase is wellestablished for the photopic range used here.9
The unexpected result is that as the luminance of thecoherent grating target is increased, the visual resolvingpower decreases. Let us first eliminate some of the poten-tial causes of this decline in acuity.
As an artificial pupil was used, there could be no opticalexplanation of this effect, as the diffraction cutoff limitwould remain constant at 82 c/deg. Furthermore, the depthof focus of the eye with a 3-mm pupil is ±0.3 D,' whichwould make changes in accommodation unimportant. Aswas discussed above, it has been shown that there is nointrinsic difference in visual physiology for coherent andincoherent light.
Now we will examine the speckle effect.
The size of the speckle on the retina, i-, is given by'8' 2 2
T= 20.3X/d, (1)
where d is the pupil diameter in millimeters.In order to establish a relationship between speckle size
(given in micrometers on the image plane) and visual acuity(in cycles/degree) on the object plane it is advisable to calcu-late either the distance (in millimeters) between two blackbars in the retinal image of the grating corresponding to eachvisual-acuity value or the frequency (in cycles/degree) of anobject grating that has a distance between bars equivalent tothe speckle size formed on its retinal image.
If the frequency of an object grating (in cycles/degree) isknown, we can also immediately find out the distance be-tween two black bars of the grating in minutes of subtendedangle, s, or in millimeters, Yo, and then calculate the samedistance, Yr, in its image on the retina.
To calculate Yr from each yo value we have used the equa-.tion
Yr = 16.7 X1iO-3 Yo. (2)
This equation is easily deduced from the relation betweenobject and image of geometric optics for objects situated 1 min front of the eye. Conversely, following the same processbut in reverse, we can take a value of yr equal to r and fromthis find the frequency of an object grating for which Yr = -T.,The results of these simple calculations, shown in Table 1,can be helpful in understanding the discussion below.
The limit to discrimination of a grating without specklecould be the modulation transfer function of the eye's opticsor the resolution limit of the retina. However, in coherentlight it is the presence of speckle in the image that sets thelimit. In our case the speckle size is -'4.3 Ain, equivalent to agrating of 34 c/deg. Table 1 shows that when luminance is 3cd/in 2
, the value of the visual acuity (33 c/deg) is close to thelimit stated by the speckle size. However, as luminanceincreases, acuity decreases in spite of the fact that the speck-le size does not vary. To explain this fact there are twooptions: either recognize that luminance has no influenceon the speckle effect and look for another explanation orassume that the effect of the speckle is dependent on theluminance.
J. M. Artigas and A. Felipe
1770 J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988
Table 1. Visual Acuity in Coherent Light of DifferentLuminancesa
Luminance Visual Acuity Speckle Size(cd/m2 ) c/deg s y,. (gm)' c/deg s T (Am)bFC
a Also shown are the values of s, yr, and r defined in the text and the spatialfrequency of a grating for which yr = T.
b Distances on the retina.I From Eq. (1).
If we follow the first option, we find no convincing expla-nation, since luminance has no influence on the optics of theeye. In addition, the way in which retinal responses changewith luminance is opposite that which must be assumed toexplain the present results. It could, perhaps, be thoughtthat a reduction in contrast would explain the diminution invisual acuity when luminance increases, but that is the sameas assuming a variation in the modulation transfer function(whether of the eye or of the retina) in that specific way,which has already been discussed and dismissed.
Therefore it remains only to consider the assumption thatthe masking effect of the speckle is dependent on the lumi-nance. Now the question is: Is it possible that the size ofthe speckle depends on the luminance? From Eq. (1) theanswer is no, but the equation considers only optical proper-ties. However, when other factors are taken into consider-ation, the answer is affirmative. These factors are foundedin studies about the photopic perception of a luminouspoint2 3 and on statistical properties of the speckle.' 8 Wecan affirm that, although the luminous point that forms thespeckle always has the same dimension [when the pupil sizeand X are kept constant in Eq. (1)], its image seems to belarger as the point becomes more and more intense. In otherwords, at high luminance levels the point spreads, becominga star. This spreading effect was studied by different au-thors in the first half of this century,23 who established that,for sources of diameter less than -1', the apparent diameterdepends only on the total flux arriving at the eye. There-fore, from a certain value of intensity upward, the apparentsize of the point no longer corresponds to the size of the Airypattern.
Fiorentini2 4 evaluated the spread of a luminous point bymeasuring the angular separation required to resolve twopoints. From these results one obtains an increment in theapparent size of the point from 1 to 3 gim, according toexperimental conditions, when the intensity is varied from10 to 400 in arbitrary units. This finding could explain ourresults, since it indicates that the apparent speckle size thatlimits the resolution of gratings increases with luminance.Thus the acuity limit imposed by speckle becomes lower infrequency.
From Table 1 one sees that the speckle is indeed a pointsource of 53" subtended angle; therefore, in photopic vision,its apparent size must be a function of the luminance. At alow luminance (3 cd/M2 ), the visual acuity corresponds to a55" distance between bars in the grating, which is approxi-
mately the speckle size. As luminance increases to values of11, 45, 100, and 400 cd/M2, the visual acuity (expressed as s)declines to 1', 1'3", 1'5", and 1'10", respectively. In ouropinion, these values may approximate the apparent size ofthe speckle at those luminance levels. If we now considerthese values in relation to distances (in micrometers) on theretina (fourth column in Table 1) we see that the variation inYr is -1.3 Am on the retina when luminance varies from 3 to400 cd/M2. This is of the same magnitude as the variation inthe apparent size of point source when luminance varies,according to Fiorentini's results.
It may be argued that the same increment in luminanceoccurs for both speckle and grating. Therefore, althoughthe speckle effect becomes more evident, unmasked resolu-tion acuity is also increasing. Why does the masking effectof speckle increase faster than unmasked acuity? Althoughthe increment in luminance is the same for both speckle andgrating, there is a significant difference. In the grating theintensity distribution is uniform from bar to bar, and wecannot find bars with an intensity higher than the meanintensity value. However, the distribution of intensity inthe speckle follows an exponential function, and the exis-tence of points in the speckle pattern with an intensityhigher than the mean value is evident.18 In the speckle, theprobability P(I) that the intensity exceeds a certain value I isgiven by
P(I) = + (I) exp(- (I )d0 = exp(-I/(I)), (3)
where (I) is the mean value. Taking, for instance, a meanvalue of (I) = 50, the probability of having I = 80 is 20%,while for the grating this probability is evidently zero.
If we consider (from Table 1) that the effect of luminanceon apparent speckle size starts from -11 cd/M2 or greater(when visual acuity begins to decrease), we can calculate theprobability of having luminances higher than 11 cd/M2 ateach luminance level of the experiment, finding that P(11) =2.6, 36.8, 78.3, 89.6, and 97.3%, respectively for the five lumi-nance levels employed (3, 11, 45, 100, and 400 cd/M2). Thisfact, associated with the spreading effect of a point source inphotopic vision, explains the decline in visual acuity as lumi-nance increases.
We think that the explanation proposed, while not exclud-ing other explanations, most closely fits the experimentalresults. Any other kind of explanation, founded, for in-stance, on the spatial-frequency selectivity-of-channels the-ory, does not seem possible given the data known atpresent.2 5
Perhaps in the near futute a miore satisfactory explanationfor these results may be tound. Notwithstanding, the re-sults of the present work set out two facts to take intoconsideration:
1. The masking effect of speckle increases with lumi-nance, and, therefore, the ability to distinguish details de-creases with luminance in the presence of laser speckle inphotopic vision.
2. When we deal with the eye, the effective size of thespeckle is not always the value calculated from its statisticalproperties, since the speckle size varies, from a practicalpoint of view, with luminance.
J. M. Artigas and A. Felipe
Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A 1771
ACKNOWLEDGMENTS
We wish to thank F. W. Campbell and the referees for theirhelpful criticism of the manuscript and the Spanish Com-mission for Scientific and Technological Research (CAI-CYT, grant 0749/81) for financial support. We would alsolike to thank Jeremy Prydal for his help in writing themanuscript in English.
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