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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

[e-mail]

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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M. Borish, "Clinical refraction", Professional Press, Chicago, 1979,

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4.

EN ISO 8597 Standard "Ophthalmic optics. Visual acuity testing - standard optotype and its presentation
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W. Johnston, "Making sense of M, N and logMAR systems specifying visual acuity", Problems in Optometry,
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H. Szydlowski, "Theory of measurements", PWN, Warszawa, 1981 [in Polish],

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M. Pluta, "Visual resolution of sinusoidal colour line patterns", SPIE Proc. 3579 (1998), pp. 48 - 52.

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