VISUAL RESOLUTION IN INCOHERENT AND COHERENT LIGHT - PRELIMINARY INVESTIGATIONS Katarzyna SARNOWSKA-HABRAT, Boguslawa DUBIK, Marek ZAJĄC Visual Optics Laboratory Institute of Physics Wroclaw University of Technology Wyspianskiego 27 PL 50-370 Wroclaw, Poland
[email protected]
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].
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 (compare ref. [8]).
Fig. 3 Schematic diagram of V.A. measurement in coloured light TEST 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. 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 δMAR RESULTS OF MEASUREMENTS Measurements of resolution in white light Table 1. Resolution limits in white light Subject
age
sex
B. D.
47
F
D. K.
26
M
A. M.
22
F
K. M.
26
F
M. Z.
50
M
K. H.
26
F
T. H.
25
M
P. J.
24
M
refraction OP: -2.75 DS., -1.25 DC. ∗ 90° OL: -3.50 DS., -0.75 DC. ∗ 95° OP: -2.50 DS., -1.25 DC. ∗ 20° OL: -1.75 DS., -1.50 DC. ∗ 90° OP: 0 OL: 0 OP: 0 OL: 0 OP: -6.00 DS., -1.50 DC. ∗ 10° OL: -5.75 DS., -1.75 DC. ∗ 170° OP: 0 OL: 0 OP: 0 OL: 0 OP: 0 OL: 0
MAR [arc min] δMAR [arc min] 1.32
0.061
1.62
0.050
1.57
0.078
0.98
0.045
1.62
0.050
1.53
0.084
1.47
0.045
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
MARrel = MARcolored / MARwhite Table 2. Relative resolution limits in broadband spectrum Subject B. D. D. K. A. M. K. M. M. Z. K. H. T. H. P. J. Average MAR Variation MAR
red filter λ=625 nm MARrel 1.03 1.00 1.18 1.37 1.10 0.96 1.16 1.00 1.100 0.135
green filter λ=565 nm MARrel 0.98 1.02 1.14 1.14 1.21 0.93 1.20 1.00 1.078 0.108
blue filter λ=475 nm MARrel 1.39 1.53 1.20 1.67 1.50 1.06 1.36 1.26 1.371 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 MARrel = MARcolored / MARwhite Table 3. Relative resolution limits in quasimonochromatic light
Subject B. D. D. K. A. M. K. M. M. Z. K. H. T. H. P. J. Average MAR Variation MAR
red λ=625 nm
yellow λ=589 nm
yellow λ=588 nm
green λ=550 nm
blue λ=475 nm
violet λ=436 nm
MARrel 1.07 0.99 1.11 1.32 1.00 0.95 1.06 1.00
MARrel 0.76 1.01 1.00 1.15 0.93 0.71 0.93 0.63
MARrel 0.74 1.02 1.14 1.32 0.90 0.74 1.21 0.63
MARrel 1.04 1.14 1.13 1.15 1.13 0.95 0.99 1.00
MARrel 1.38 1.41 1.22 1.81 1.67 0.93 1.29 1.25
MARrel 2.01 1.96 1.82 1.98 2.02 1.36 1.41 1.76
1.063
0.980
0.963
1.066
1.370
1.790
0.116
0.175
0.250
0.080
0.273
0.267
Fig. 5 Relative resolution measured in coloured light versus the mean wavelength
HYPHOTHESES We wanted to check whether the values of MAR measured in light of different colours differ substantially. The values of MARrel 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 MARrel 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 MARrel 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' = 2α= 0.01) we have critical value of parameter t equal tr,α = 3.500. For the level of significance α = 0.05 critical value of parameter t is tr,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 T tr,α = 3.500 tr,α = 1.895
red broadband λ=625 nm 2.095
green blue red Yellow yellow green blue violet broadbroadmonochr. monochr. monochr. monochr. monochr. monochr. band band λ=625 nm λ=589 nm λ=588 nm λ=550 nm λ=475 nm λ=436 nm λ=565 nm λ=475 nm 2.043 5.354 1.536 0.323 0.419 2.333 3.833 8.369
t < tr,α
t < tr,α
t > tr,α
t < tr,α
t < tr,α
t < tr,α
t < tr,α
t > tr,α
t > tr,α
t > tr,α
t > tr,α
t > tr,α
t < tr,α
t < tr,α
t < tr,α
t > tr,α
t > tr,α
t > tr,α
CONCLUSION 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 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 MARrel = MARcolored / MARwhite Table 5. Relative resolution limits in quasimonochromatic incoherent and coherent light MARcoherent -----------Spectral lamp, λ=625 nm Laser light, λ=633 nm Subject MARincoherent MARrel MARrel δ MAR δ MAR B. D. D. K. A. M. K. M. M. Z. K. H. T. H. P. J. Average MAR Variation MAR
1.07 0.99 1.11 1.32 1.00 0.95 1.06 1.00
0.078 0.045 0.071 0.050 0.050 0.050 0.082 0.050
1.21 0.97 1.19 1.37 1.18 1.14 1.19 1.14
0.061 0.078 0.084 0.078 0.145 0.071 0.071 0.071
1.131 0.980 1.072 1.038 1.180 1.200 1.123 1.140 1.1079 0.0737
HYPHOTHESIS We wanted to check whether the values of MAR measured in incoherent and coherent light differ substantially. For almost all Subjects the values of MARrel measured in incoherent light (i.e. spectral lamp with interference filter) are lower than the values of MARrel measured in coherent, laser light. Their ratio MARcoherent / MARincoherent 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 MARcoherent / MARincoherent 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 = n1 = 7 and level of significance α = 0.005 (α' = 2α= 0.01) we have critical value of parameter t equal tr,α = 3.500. Then we calculated the value of statistical parameter t for MARcoherent / MARincoherent from the formula (1). The result is: t = 4.141 > tr,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, TwymanGreen 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. 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.
Paper surface Subject
B. D. D. K. A. M. K. M. M. Z. K. H. T. H. P. J. Average MAR Variation MAR
MAR [arc min]l 2.17 2.38 2.47 1.97 2.24 2.05 2.23 2.09 2.200 0.167
δ MAR 1.0 1.7 1,9 1.0 0.9 1.0 0.9 1.3
Ground glass roughness #100 MAR [arc min] 2.12 2.38 3.51 2.37 2.50 2.67 2.53 1.94 2.503 0.469
δ MAR 0.8 1.3 4.1 1.3 1.0 1.6 0.9 1.7
Ground glass roughness #800 MAR [arc min] 2.00 2.24 2.92 2.44 2.58 2.60 2.41 1.96 2.394 0.321
δ MAR 0.5 1.0 1.3 0.9 1.5 1.0 1.1 1.7
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 MARrel = MARinterference / MARwhite 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.
Subject
B. D. D. K. A. M. K. M. M. Z. K.H. T.H. P.J. Average MAR Variation MAR
paper
Interference fringes Ground glass #100 Ground glass #800
MARrel
MARrel
MARrel
1.64 1.47 1.57 2.01 1.38 1.34 1.52 1.62
1.61 1.47 2.24 2.42 1.54 1.75 1.72 1.50 1.6875 0.3099
1.52 1.38 1.86 2.49 1.59 1.70 1.64 1.52
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 (seeing 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 (n1 = n2 = 8) we have to use Student's t-distribution. Assuming number of degrees of freedom r = n1+n2-2 = 14 and level of significance α = 0.01 we have critical value of parameter tr,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 < tr,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 < tr,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 MARinterference / MARwhite 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' = 2α= 0.01) we have critical value of parameter t equal tr,α = 3.500. Then we calculated the value of statistical parameter t for MARcoherent / MARincoherent from the formula (1). The result is: t = 10.869 > tr,α = 3.500, which means that we cannot assume that both mean values of MAR are the same. 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. REFERENCES G. Smith, D. A. Atchinson, "The eye. Visual optical instruments", Cambridge University Press, Cambridge 1997. 2. M. Borish, "Clinical refraction", Professional Press, Chicago, 1979. 3. Arditi, R. Cagenello, "On the statistical reliability of letter-chart visual acuity measurements", Investigative Ophthalmology & Visual Science, 34 (1993), pp. 120-129. 4. EN ISO 8597 Standard "Ophthalmic optics. Visual acuity testing - standard optotype and its presentation (1994). 5. W. Johnston, "Making sense of M, N and logMAR systems specifying visual acuity", Problems in Optometry, 3 (1991), pp. 394-404. 6. E. M. Lowry, J. J. De Palma, "Sine-wave response of the visual system. I - The Mach phenomenon", J. Opt. Soc. Am., 51 (1961), pp. 740-746. 7. J. J. De Palma, E. M. Lowry, "Sine-wave response of the visual system. II - Sine wave and square wave contrast sensitivity", J. Opt. Soc. Am., 52 (1962), pp. 328-335. 8. K. Sarnowska-Habrat, M. Zając, B. Dubik, "Measurement of visual acuity in different illumination conditions" presented on the conference Physiological Optics PHO’99 held in September 1999 in Wrocław, Poland. 9. H. Szydlowski, "Theory of measurements", PWN, Warszawa, 1981 [in Polish]. 10. M. Pluta, "Visual resolution of sinusoidal colour line patterns", SPIE Proc. 3579 (1998), pp. 48 - 52. 11. L. N. Thibos, A. Bradley, D. K. Still, "Interferometric measurement of visual acuity and the effect of ocular chromatic aberrations", Appl. Opt, 30 (1991), pp. 2105 - 2116. 12. M. śarowska, "Investigation of the influence of coherence on vision quality", MSc Thesis, Institute of Physics, Wroclaw University of Technology, Wroclaw, 2000 [in Polish]. 1.
