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VISUAL RESOLUTION
IN INCOHERENT AND COHERENT LIGHT
- PRELIMINARY INVESTIGATIONS
Katarzyna SARNOWSKA-HABRAT, Boguslawa DUBIK, Marek ZAJAC
Visual Optics Laboratory
Institute of Physics
Wroclaw University of Technology
Wyspianskiego 27
PL 50-370 Wroclaw, Poland
zajac@if.pwr.wroc.pl
ABSTRACT
In ophthalmology and optometry a number of measures is used for describing quality of human vision such as
resolution, visual acuity, contrast sensitivity function etc. In this paper we will concentrate on the vision quality
understood as a resolution of periodic object being a set of equidistant parallel lines of given spacing and direction.
The measurement procedure is based on presenting the test to the investigated Subject and determining the highest
spatial frequency he/she can still resolved. In this paper we describe a number of experiments in which we used test
tables illuminated with light of different spectral characteristics both coherent and incoherent. Our experiments
suggest that while considering incoherent polychromatic illumination the resolution in blue light is substantially
worse than in white light. In coherent illumination speckling effect causes worsening of resolution.
While using laser light it is easy to generate a sinusoidal interference pattern, which can serve as test object. In the
paper we compare the results of resolution measurements with test tables and interference fringes.
INTRODUCTION
Human vision is a complex process involving a number of different systems: an eyeball as image forming system, a
retina as detecting system, optical nerves as signal transmitting system, a brain as interpreting and controlling system.
All those systems influence the whole process of vision [1, 2].
The term "Quality of Vision" is not explicit since its meaning depends on which particular feature of vision is the
most interesting for us, e.g.: colour discrimination, movement detection, evaluation of distances and directions,
objects recognition etc.
In optometry and ophthalmology Visual Acuity (V.A.) is used to describe quality of vision. It relates to the ability of
recognition of small objects of high contrast i.e. their discriminating from the background and identification. Central
(foveal) vision is typically assumed.
In general the results of V.A. measurements depend on the kind of the test objects (its shape, orientation,
neighbourhood etc.) since the recognition is influenced not only by the "optical" quality of retinal image, but also by
the psychological process of image interpretation. To avoid misunderstandings the careful choice of test objects is of
great importance [3]. Some simple objects (Optotypes) are used widely: letters, numbers or simple graphical symbols,
two of them being preferred: Landolt ring (C) and Snellen hook (E) [4]. The measure of V.A. is the size (angular) of
the smallest detail of the Optotype correctly recognised. In can be expressed as Snellen Fraction (V = L/D) defined as
the ratio of distance L from which the optotype would be seen under the angle equal to 5 min of arc to the actual
observation distance D. The alternative measures are: MAR (Minimum Angle of Resolution) equal to the angular size
of the smallest recognised detail of optotype or its logarithm denoted by logMAR (Figure 1) [5].
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Fig. 1 Visual Acuity concept
The test object preferred by us, however, is periodic lineal test of high contrast (possibly close to 1) such as Ronchi
Ruling (Figure 2) or Sinusoidal Pattern [6,7]. It is easily reproducible and measurable. Moreover probably its
recognition does not need involving any advanced psychological processes for recognition and the result of V.A.
measurement depends mainly on the quality of retinal image (including its detection to some extent).
The periodic test chart is presented to the Subject who is expected to state if he/she can resolve any directional
structure on the presented test chart or not - only uniform grey field is seen.
Fig. 2 Periodic test for measuring Visual Acuity
In this paper we wanted to check how the measured V.A. depends on the physical parameters of the illuminating light
such as its colour and state of coherence.
EXPERIMENT No. 1
In this experiment we wanted to measure Visual Acuity using tests illuminated with light of different spectral content.
The schematic diagram of an experimental set-up is presented in the Figure 3 (comp. [8]).
Fig. 3 Schematic diagram of V.A. measurement in coloured light
TEST
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Test objects: Rectangular ruling (parallel equidistant black-and-white, high contrast stripes printed on a smooth
silky paper with high quality laser printer).
Test size: 16 cm x 16 cm.
Test orientation: up, down, right, left in random order,
Test spatial frequencies: 1, 2, 3, 4, 5, 6, 7, 8, 9 l/mm.
Test background: dark (black) surface.
Viewing distance: 4.25 m.
Angular test size: 2
°
Illumination: with different light sources listed below
LIGHT SOURCES
Halogen microscopy lamp emitting white light, illumination 300 lx;
Halogen microscopy lamp with broad-band absorption filters (GamColor
, see Figure 4)
red (dominant wavelength
λ
= 625 nm, T = 7.7%),
green (dominant wavelength
λ
= 565 nm, T = 36%),
blue (dominant wavelength
λ
= 475 nm, T = 4%);
Fig. 4 Spectral characteristics of broadband filters used in Experiment 1
Sodium spectral lamp (
λ
= 589 nm);
High-pressure mercury lamp with interference filters (half width 10 nm)
red (
λ
= 625 nm),
yellow (
λ
= 588 nm,
green (
λ
= 550 nm),
blue (
λ
= 475 nm,
violet (
λ
= 436 nm)
SUBJECTS:
8 persons, four females and four males of different age. Some emmetropes, the others wearing their normal
correction glasses. All with normal colour vision.
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PROCEDURE
Few minutes of adaptation to darkness,
Binocular vision,
No head restriction,
Presentation of tests in order of increasing spatial frequency beginning from the highest until the Subject
recognises the striped structure and indicate its correct direction,
Presentation of tests in order of decreasing spatial frequency beginning from the lowest until the Subject sees
uniform grey (coloured) field without noticeable directional structure,
10 - 20 times of repetition, calculation of average MAR and its variation
δ
MAR
RESULTS OF MEASUREMENTS
Measurements of resolution in white light
Table 1. Resolution limits in white light
Subject
age
sex
Refraction
MAR
[arc min]
δ
MAR
[arc min]
B. D.
47
F
OP: -2.75 DS., -1.25 DC.
∗
90
°
OL: -3.50 DS., -0.75 DC.
∗
95
°
1.32
0.061
D. K.
26
M
OP: -2.50 DS., -1.25 DC.
∗
20
°
OL: -1.75 DS., -1.50 DC.
∗
90
°
1.62
0.050
A. M.
22
F
OP: 0
OL: 0
1.57
0.078
K. M.
26
F
OP: 0
OL: 0
0.98
0.045
M. Z.
50
M
OP: -6.00 DS., -1.50 DC.
∗
10
°
OL: -5.75 DS., -1.75 DC.
∗
170
°
1.62
0.050
K. H.
26
F
OP: 0
OL: 0
1.53
0.084
T. H.
25
M
OP: 0
OL: 0
1.47
0.045
P. J.
24
M
OP: 0
OL: 0
1.29
0.050
We wanted to compare resolution in coloured broadband spectrum light with the resolution in white light. In
order to compensate the influence of different visual acuities of particular Subjects we calculated RELATIVE
resolution i.e. divided the measured MAR in coloured light by MAR measured in white light
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MAR
REL
= MAR
COLORED
/ MAR
WHITE
Table 2. Relative resolution limits in broadband spectrum
Subject
red filter
λ
=625 nm
green filter
λ
=565 nm
blue filter
λ
=475 nm
MAR
REL
MAR
REL
MAR
REL
B. D.
1.03
0.98
1.39
D. K.
1.00
1.02
1.53
A. M.
1.18
1.14
1.20
K. M.
1.37
1.14
1.67
M. Z.
1.10
1.21
1.50
K. H.
0.96
0.93
1.06
T. H.
1.16
1.20
1.36
P. J.
1.00
1.00
1.26
Average MAR
1.100
1.078
1.371
Variation MAR
0.135
0.108
0.196
We wanted to compare resolution in coloured quasimonochromatic light and the resolution in white light. In
order to compensate the influence of different visual acuities of particular Subjects we calculated RELATIVE
resolution i.e. divided the measured MAR in coloured light by MAR measured for white light
MAR
REL
= MAR
COLORED
/ MAR
WHITE
Table 3. Relative resolution limits in quasimonochromatic light
Subject
red
λ
=625 nm
yellow
λ
=589 nm
yellow
λ
=588 nm
green
λ
=550 nm
blue
λ
=475 nm
violet
λ
=436 nm
MAR
REL
MAR
REL
MAR
REL
MAR
REL
MAR
REL
MAR
REL
B. D.
1.07
0.76
0.74
1.04
1.38
2.01
D. K.
0.99
1.01
1.02
1.14
1.41
1.96
A. M.
1.11
1.00
1.14
1.13
1.22
1.82
K. M.
1.32
1.15
1.32
1.15
1.81
1.98
M. Z.
1.00
0.93
0.90
1.13
1.67
2.02
K. H.
0.95
0.71
0.74
0.95
0.93
1.36
T. H.
1.06
0.93
1.21
0.99
1.29
1.41
P. J.
1.00
0.63
0.63
1.00
1.25
1.76
Average
MAR
1.063
0.980
0.963
1.066
1.370
1.790
Variation
MAR
0.116
0.175
0.250
0.080
0.273
0.267
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Fig. 5 Relative resolution measured in coloured light versus the mean wavelength
HYPOTHESES
We wanted to check whether the values of MAR measured in light of different colours differ substantially. The
values of MAR
rel
for red, green and yellow colours collected in Tab. 1 and Tab. 2 fall to the interval [0.96 - 1.10], so
are close to unity. This suggests that the resolution limit measured in these colours is the same as in white light. The
values of MAR
rel
for blue and violet collected in Tab. 1 and Tab 2 are greater than 1.30 This suggests, that the
resolution limit measured in these colours is higher than in white light - visual acuity is blue end of spectrum is worse.
Vision quality in red, yellow and green lights are the same as in white light (independently whether the spectrum
is broadband or narrow - quasimonochromatic).
Vision quality in blue light is substantially worse than in white light.
VERIFICATION
We used statistical analysis [9] to verify the hypothesis that mean value of measured MAR
rel
does not differ
substantially from 1 with alternative hypothesis that it is greater than 1. Since the number of samples (i.e. investigated
Subjects) is small (n = 8) we had to use Student's t-distribution. Assuming number of degrees of freedom r = n-1 = 7
and level of significance
α
= 0.005 (
α
'
=
2
α
= 0.01) we have critical value of parameter t equal t
r,
α
= 3.500. For the
level of significance
α
= 0.05 critical value of parameter t is t
r,
α
= 1.895. Then we calculated the values of statistical
parameter t for series of MAR measurements in different colours from the formula:
(1)
The results are as follows (Tab. 4):
Table 4.Values of statistical parameter t Relative resolution limits in quasimonochromatic light
light
red broad-
band
λ
=625 nm
green
broad-
band
λ
=565 nm
blue
broad-
band
λ
=475 nm
red
monochr.
λ
=625 nm
Yellow
monochr.
λ
=589 nm
yellow
monochr.
λ
=588 nm
green
monochr.
λ
=550 nm
blue
monochr.
λ
=475 nm
violet
monochr
λ
=436 nm
T
2.095
2.043
5.354
1.536
0.323
0.419
2.333
3.833
8.369
t
r,
α
= 3.500
t < t
r,
α
t < t
r,
α
t > t
r,
α
t < t
r,
α
t < t
r,
α
t < t
r,
α
t < t
r,
α
t > t
r,
α
t > t
r,
α
t
r,
α
= 1.895
t > t
r,
α
t > t
r,
α
t > t
r,
α
t < t
r,
α
t < t
r,
α
t < t
r,
α
t > t
r,
α
t > t
r,
α
t > t
r,
α
CONCLUSION
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We can state with 99.5% probability that the Visual Acuity in blue light is worse that in white. We may also state that
with 95% probability, that in green light Visual Acuity is worse than in white. However Visual Acuity in yellow and
in red is almost the same as in white. This conclusion is in accordance with results reported in other papers [e.g. 10].
EXPERIMENT No. 2
In this experiment we wanted to measure Visual Acuity using tests illuminated with coherent and incoherent light of
the same colour. We used the same experimental set-up as in the Experiment No.1 but exchanged the illuminating
lamp onto He-Ne laser with beam expander.
TEST
The same as in the Experiment No. 1
LIGHT SOURCES
High-pressure mercury lamp with red interference filter (
λ
= 625 nm, half width 10 nm)
He-Ne, 5 mW laser (
λ
= 633 nm)
SUBJECTS
8 persons, the same as in the Experiment No. 1
PROCEDURE
The same as in the Experiment No. 1
RESULTS
We wanted to compare resolution in incoherent and coherent light independently on the different visual acuities of
particular Subjects, therefore we calculated RELATIVE resolution i.e. divide the measured MAR in coloured
(incoherent or coherent) light by MAR measured in white light
MAR
REL
= MAR
COLORED
/ MAR
WHITE
Table 5. Relative resolution limits in quasimonochromatic incoherent and coherent light
Subject
Spectral lamp,
λ
=625 nm
Laser light,
λ
=633 nm
MAR
COHERENT
---------------------
MAR
INCOHERENT
MAR
REL
δ
MAR
MAR
REL
δ
MAR
B. D.
1.07
0.078
1.21
0.061
1.131
D. K.
0.99
0.045
0.97
0.078
0.980
A. M.
1.11
0.071
1.19
0.084
1.072
K. M.
1.32
0.050
1.37
0.078
1.038
M. Z.
1.00
0.050
1.18
0.145
1.180
K. H.
0.95
0.050
1.14
0.071
1.200
T. H.
1.06
0.082
1.19
0.071
1.123
P. J.
1.00
0.050
1.14
0.071
1.140
Average
MAR
1.1079
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Variation
MAR
0.0737
HYPOTHESIS
We wanted to check whether the values of MAR measured in incoherent and coherent light differ substantially.
For almost all Subjects the values of MAR
rel
measured in incoherent light (i.e. spectral lamp with interference filter)
are lower than the values of MAR
rel
measured in coherent, laser light. Their ratio MAR
COHERENT
/ MAR
INCOHERENT
is given in the last column of Table 5. The mean value of this ratio is greater than 1. This result suggests that Visual
Acuity in laser light is lower (we see worse) than in incoherent light
VERIFICATION
We used statistical analysis [9] to verify the hypothesis that mean value of MAR
COHERENT
/ MAR
INCOHERENT
equals 1 with alternative hypothesis, that it is greater than 1. Since the number of samples (i.e. investigated Subjects)
is small (n = 8) we had to use Student's t-distribution. Assuming number of degrees of freedom r = n-1 = 7 and level
of significance
α
= 0.005 (
α
'
=
2
α
= 0.01) we have critical value of parameter t equal t
r,
α
= 3.500. Then we calculated
the value of statistical parameter t for MAR
COHERENT
/ MAR
INCOHERENT
from the formula (1). The result is:
t = 4.141 > t
r,
α
= 3.500, which means that we cannot assume that both mean values of MAR are the same.
CONCLUSION
We can state with 99.5% probability that Visual Acuity measured in laser light is worse than in incoherent,
quasimonochromatic light of the some mean wavelength. The most probable reason for it is speckling effect.
EXPERIMENT No. 3
Using laser light one can easily generate sinusoidal fringes of different spacing and direction. To this aim we used
several interferometric set-ups such as polarisation Wollaston interferometer, Michelson interferometer, Twyman-
Green interferometer, Mach-Zechnder interferometer or shearing interferometer. In each case it is easy to change the
spacing and orientation of fringes observed on the screen by simple movement of single element. After several trials
we chose the shearing interferometer as presented in the Figure 6. The spacing of fringes was changed by shifting the
collimating lens along the optical axis. The shift, done by electric motor, could be controlled either by an
experimenter or by the Subject. Due to changes in wavefront curvature the observed fringes were slightly bent, but
this effect did not disturb the measurement in practice.
Fig. 6 Twyman-Green interferometer used for generation of sinusoidal test pattern
TEST
Sinusoidal fringes generated in Mach-Zechnder interferometer. Three screen materials were used: white silky
paper and 2 glass plates of different roughness (grinded with powder of granularity #800 and #100). The test pattern
created on a screen has 15 cm diameter and was observed from the distance 4.25 m (angular extension of the test 2 arc
mins). The average intensity of fringe pattern falls gradually to zero, so it has no sharp boundary. Such situation is
more convenient for visual resolution measurement.
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LIGHT SOURCE
He-Ne, 5 mW laser (
λ
= 633 nm)
SUBJECTS:
8 persons, the same as in the Experiment No. 1
PROCEDURE
The Subject changed the spacing of the fringes by shifting the collimating lens until the critical value of spatial
frequency was found i.e. the directional structure of the test was barely resolved.
The measurements were performed about dozet times for three screens of different roughness.
RESULTS
We want to compare the resolution measured with help of sinusoidal interference fringes with the resolution
measured with help of typical binary black-and-white lineal test. We wanted also to check the influence of the screen
structure on the measurements result. In the Table 6 we collect the result of measurements.
Table 6. Resolution limits - measured with interference fringes on different surfaces.
Subject
Paper surface
Ground glass roughness
#100
Ground glass roughness
#800
MAR [arc
min]
l
δ
MAR
MAR [arc
min]
δ
MAR
MAR [arc
min]
δ
MAR
B. D.
2.17
1.0
2.12
0.8
2.00
0.5
D. K.
2.38
1.7
2.38
1.3
2.24
1.0
A. M.
2.47
1,9
3.51
4.1
2.92
1.3
K. M.
1.97
1.0
2.37
1.3
2.44
0.9
M. Z.
2.24
0.9
2.50
1.0
2.58
1.5
K. H.
2.05
1.0
2.67
1.6
2.60
1.0
T. H.
2.23
0.9
2.53
0.9
2.41
1.1
P. J.
2.09
1.3
1.94
1.7
1.96
1.7
Average
MAR
2.200
2.503
2.394
Variation
MAR
0.167
0.469
0.321
The data from Table 6 can be used for checking if the roughness of the screen surface influences the
measurement result. For comparison of this measurement with the measurement performed in white light however it
is better to calculate the RELATIVE resolution i.e. to divide the measured MAR with help of interference fringes
MAR measured in white light
MAR
REL
= MAR
INTERFERENCE
/ MAR
WHITE
In this way we took into account different acuities of particular Subjects. The normalised data are collected in the
Table 7.
Table 7. Relative resolution limits - measured with interference fringes on different surfaces.
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Subject
Interference fringes
paper
Ground glass
#100
Ground glass
#800
MAR
rel
MAR
rel
MAR
rel
B. D.
1.64
1.61
1.52
D. K.
1.47
1.47
1.38
A. M.
1.57
2.24
1.86
K. M.
2.01
2.42
2.49
M. Z.
1.38
1.54
1.59
K.H.
1.34
1.75
1.70
T.H.
1.52
1.72
1.64
P.J.
1.62
1.50
1.52
Average MAR
1.6875
Variation
MAR
0.3099
HYPOTHESES
We want to check whether screen material influences the measured value of MAR. The data from Table 6
suggest that there is no such influence.
We want to compare the results of MAR measurements with help of interference fringes with results of MAR
measurements in white light. The data from Table 7 suggest that values of MAR measured with interference fringes
are higher so the Visual Acuity is lower (vision is worse).
VERIFICATION
We use statistical analysis [9] to verify the hypothesis that mean values of MAR
measured for different kinds of
screen material are the same with alternative hypothesis, that they are different. Since the number of samples (i.e.
investigated Subjects) is small (n
1
= n
2
= 8) we have to use Student's t-distribution. Assuming number of degrees of
freedom r = n
1
+n
2
-2 = 14 and level of significance
α
= 0.01 we have critical value of parameter t
r,
α
= 2.977. Then we
calculate the value of statistical parameter t for particular pairs of MAR measurements from the formula:
(2)
The result are:
For ground glass #100 and ground glass #800 the value of statistic parameter t is t = 0.542 < t
r,
α
= 2.977, which
means that we can assume that both the mean values of MAR are equal
For paper screen and ground glass #100 te value of statistic parameter t is t = 1.721 < t
r,
α
= 2.977, which means
that we can assume that both the mean values of MAR are equal
We used statistical analysis [9] to verify the hypothesis that mean value of MAR
interference
/ MAR
white
equals 1
with alternative hypothesis, that it is greater than 1. Since the number of samples (i.e. investigated Subjects) is small
(n = 8) we had to use Student's t-distribution. Assuming number of degrees of freedom r = n-1 = 7 and level of
significance
α
= 0.005 (
α
'
=
2
α
= 0.01) we have critical value of parameter t equal t
r,
α
= 3.500. Then we calculated
the value of statistical parameter t for MAR
coherent
/ MAR
incoherent
from the formula (1). The result is: t = 10.869 > t
r,
α
= 3.500, which means that we cannot assume that both mean values of MAR are the same.
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CONCLUSION
We can state with 99% probability that the material of a screen on which the interference fringes are observed has no
influence on the results of MAR measurements.
The Visual Acuity measured on interference fringes in laser light is worse than in incoherent, white light by about
60%. The most probable reason for it is speckling effect.
It is known that character of speckles depend on two factors: statistic properties of diffusing screen and the relative
aperture of imaging system (the speckle size being inversely proportional to the aperture). It seems that in our
experiments the average diameter of eye pupil was so small that the influence of diffusing screen structure on speckle
size is negligibly small in comparison to the influence of pupil size.
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