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Visual perception of the Moiréeffect
Ophthal. Physiol. Opt. Vol. 19, No. 5, pp. 427±430, 1999 # 1999 The College of Optometrists. Published by Elsevier Science Ltd All rights reserved. Printed in Great Britain 0275-5408/99 $20.00 + 0.00
PII: S0275-5408(99)00016-2
Research Note Visual perception of the Moire effect Pedro MunÄoz and Javier Alda  ptica, Universidad Complutense de Madrid, Escuela Universitaria de O  ptica, Departamento de O Avda, Arcos de JaloÂn s/n, 28037, Madrid, Spain Summary The perception of Moire fringes is studied with two different tests for binocular and monocular conditions. The results are negative for binocular conditions, and positive for the monocular case when afterimages are used. # 1999 The College of Optometrists. Published by Elsevier Science Ltd. All rights reserved
Introduction
Moire fringes are obtained any time two periodic signals are superimposed multiplicatively (in opposition to interference where the superposition is made additively). In optics, the Moire eect can be observed by placing together two similar periodical transmittances. The total transmittance is obtained by multiplying the individual ones. When the transmittances are superimposed almost in the same conditions the total transmittance shows a periodic variation whose orientation, pitch, and shape depends on the relative orientation, pitch and shape of the individual transmittances. The general treatment and some applications of the Moire eect are extensively reported in several books and papers (Kafri and Glatt, 1990; Creath and Wyant, 1992 and references therein). In the research reported here two identical square gratings were used. They were rotated with a small angle between them. This particular case allows a simpler treatment than the general one. The Moire fringes are observed oriented parallel to the bisectrix of the angle between the gratings. The period of the Moire fringes, pMoire is p , related with the period of the gratings as, pMoire 2sina where 2a is the angle between the gratings, and p the spatial period of the individual gratings. The perception of gratings in binocular conditions has been studied previously by several authors. Some previous works have been reported using two periodic gratings with a relative orientation of 908 (Wade, 1974; O'Shea et al., 1997). These papers studied the relation between rivalry, fusion, and stereopsis. Our case is
The study and development of an accurate algorithm to model the binocular function constitutes a challenging task for many researchers. As part of the binocular vision, the stereopsis function has been described as a non linear function of the signals representing the images of both eyes (Marr and Poggio, 1979). Several models have been developed to describe correspondence areas, rivalry, suppression, dominance, fusion, along with their thresholds to trigger a given perception (Quiang and Zhu, 1997; and references therein). Some models use correlations and multiplicative terms between the left and right eye images. Jenkin and Jepson (1998) propose a local phase function obtained from the multiplication of the two images to describe the binocular disparity. This function resembles closely the formalism that describes the Moire eect (Creath and Wyant, 1992). In this case the Moire based experiments would be a tool used to understand how those processes work. Our paper tries to contribute to this topic with a couple of basic experimental tests based on the Moire eect. Correspondence and reprints requests to: Dr J. Alda, University of Central Florida, School of Optics, PO Box 162700, Orlando, FL 32816-2700, USA. Tel.: +34-91-394-6874; fax: +34-91-394-6885, email: j.alda@®s.ucm.es Received: 20 May 1998 Revised form: 4 January 1999 Accepted: 2 February 1999
427
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Ophthal. Physiol. Opt. 1999 19: No 5
rather dierent. We are looking for the perception of the Moire eect that should be perceived when the gratings are oriented almost parallel and the perception is sensitive to some multiplicative term between monocular images. Our ®rst trials were in binocular conditions. We presented to each eye two identical gratings with a relative orientation able to induce the Moire eect if the perception process is able to handle both images in the proper way. In the experiment the results were all negative. We also carried out a second experiment that used a single grating presented monocularly. The grating was used to evoke an afterimage that was superimposed with the real image of the same grating slightly rotated. In this case our objective was to ®nd out the monocular perception of Moire fringes with afterimages. Afterimages of square gratings were used in the past to override the rivalry mechanism and produce fusion of two very dierent objects. Again, the Wade experiment (Wade, 1973, 1977) was quite dierent to ours because he used afterimages in binocular conditions. With this second experiment we could demonstrate the perception of Moire fringes in monocular conditions: all the observers perceived the Moire fringes.
Materials and methods The gratings were generated by using a postscript code in a laser printer with a resolution of 600 600 dots per inch. To obtain a transmissivity grating the printing was done on an acetate transparency. In the case of re¯ectivity gratings the printing was on regular white paper. The gratings obtained were square shaped with three spatial periods. These three spatial periods correspond with three angular frequencies that are presented in Table 1 (a set of angular frequencies for each experiment). The transmittance gratings were ®xed with two square glass windows to ®t the space given by the holder of a sinoptophor. The sinoptophor was used in the binocular test. The observers were chosen once some selective tests were made. The visual accuity, after compensation of ametropies, was 1.00 or better. The binocular function and the fusion were also tested by means of typical
superposition tests using the sinoptophor. After this, a group of 28 people were selected. They were second and third year students of the School of Optics of Madrid, with ages ranging between 20 and 25 years. There were 12 male and 16 female. Before the test, we showed them what the Moire eect looked like and what the test was that we were conducting. Test of binocular fusion of gratings The objective of this test was to know if some multiplicative terms were perceived in a binocular scene (Foley, 1991; Jenkin and Jepson, 1988; Quiang and Zhu, 1997; Wandel, 1995). Two identical transmissivity gratings were placed in the arms of the sinoptophor and rotated to each other in order to achieve an angle, 2a, able to generate four or ®ve Moire fringes in the ®eld of view (see Table 1). The gratings were placed neither in horizontal nor in vertical orientation in order to avoid any preferential orientation of the perception (Wade, 1974; Kitterle and Thomas, 1980). The patterns were presented haploscopically, focused at in®nity, with a subtended angle of 58 that assured a foveal vision. The gratings were presented in photopic conditions for 20 to 25 sec. During the ®rst 10 sec the observer had to see the gratings, and during the second half of the observation he/she should explain what he/ she was perceiving. After the test, they were asked to draw a scheme of what they perceived. The test was carried out three or four times for each observer. Monocular test based on afterimages After the negative result obtained in the previous test we developed another one using afterimages. The same group of observers were trained to recognize the postimages and become familiar with their appearance. In order to improve the contrast of the black and white areas of the gratings, a set of diuse re¯ective patterns were printed on white paper having a size of 15.2 15.2 cm2 with the same spatial periods presented in Table 1. The observer was placed staring with only one eye (the other is obtured) at the middle of the test at a distance of about 40 cm. These near ®eld con-
Table 1. Spatial and angular frequencies of the tests p2 Dp (cm)
a (deg)
Angular frequency binocular test (cycle/deg)
Angular frequency monocular test (cycle/deg)
0.292 0.01 0.212 0.02 0.142 0.03
138 108 78
2.2 2.9 4.2
2.4 3.3 5.0
p and Dp are the spatial period and the error of it. a represents the angle between gratings that it is necessary to set in the sinoptophor to get the desired Moire fringes. The angular frequencies for each one of the tests is calculated for each one of the gratings
Visual perception of the Moire effect: P. MunÄoz and J. Alda
429
the dierent groups is uncorrelated with age, sex, or ametropy. For the monocular test with afterimages the results were all positive, 100% of the observers reported the vision of the Moire fringes with the three spatial frequencies gratings.
Discussion
Figure 1. Distribution of the observers with respect to the perceived effect. Along with the distribution two insets of what the observers reported are presented, (a) and (b). The partial suppression inset (b) tries to show how different areas of the visual field behave in a different form. The symmetry and location of these areas changed from one individual to another and the inset only tries to schematize the perceived scene in a very simple way.
ditions assured that the foveal area was over®lled with a test extending over a 208 angle. Then a ¯ash lamp was triggered to evoke the postimage. Immediately the test was rotated by an approximate angle of 38 or 48. After this the observer is asked to describe what he/ she is perceiving. Before the ¯ash the room was under mesopic condition and it was switched to photopic condition after the ¯ash.
Results For the test of binocular fusion of gratings the results were negative in all individuals and none perceived the Moire fringes. Twelve observers said that the gratings were perceived alternating the right and left eye images showing a temporal evolution of their dominance±suppression eects for each eye. Thirteen observers perceived a mixed scene with spatial alternate suppression areas where one of the eyes dominates the perception. The distribution of these areas was dierent for each individual (see inset (b) of Figure 1 where we have shown a schematic representation of the results. The actual perception was more irregular in shape and location). Only two observers, who also presented a remarkable ocular dominance, perceived only the grating of his/her predominant eye, and only that part of the other grating not obscured by the dominant eye could be seen by the non dominant eye (see inset (a) of Figure 1). One of the observers was unable to describe what he was perceiving in the repeated trials. The distribution of people among
Within our experimental conditions the negative results in the binocular test show that rivalry between the images of both eyes has precluded the perception of the Moire eect. Although Moire fringes were not observed, the disparity itself could be evaluated by a multiplicative term (Jenkin and Jepson, 1988), whose phase triggers the suppression±dominance eects and avoids fusion. Therefore, our results conclude that multiplicative terms of both images were not perceived. So, if they are used in the binocular function they would be processed in a ®rst stage of the algorithm, to provide a given signal for enabling or disabling the fusion between both eyes. The positive results in the afterimages monocular test can be interpreted in the retinian level. The afterimage produces a saturation with a periodic spatial structure in the photoreceptor mosaic. Then, when a similar periodic stimulus is presented, the irradiance distribution in the retina is detected by a spatially periodic function in a multiplicative way, showing the characteristic Moire pattern. Acknowledgements The authors are very grateful to the 28 students of the School of Optics who participated in the trial. We also appreciate very much the helpful discussions with Dr. Jose Alonso and Dr. Cinta Puell during the time this paper was written.
References Creath, K. and Wyant, J. C. (1992). Moire and fringe projection techniques. ed. D. Malacara. In: Optical Shop Testing, John Wiley and Sons, New York, NY, USA, pp. 653±686. Foley, J. M. (1991). Binocular Space Perception. ed. D. Rega. In: Binocular Vision, CRC Press, Boca RatoÂn, FL, USA, pp. 75±92. Jenkin, M. R. M. and Jepson, A. D. (1988). The measurement of binocular disparity. ed. Z. W. Pylyshyn. In: Computational Processes in Human Vision, Ablex Publishing Corp., Norwood, NJ, USA, pp. 69±98. Kafri, O. and Glatt, I. (1990). The Physics of Moire Metrology, John Wiley and Sons, New York, NY, USA. Kitterle, F. L. and Thomas, J. (1980). The eects of spatial frequency, orientation, and color upon binocular rivalry
430
Ophthal. Physiol. Opt. 1999 19: No 5
and monocular pattern alternation. Bulletin of the Psychonomic Society 16, 406±407. Marr, D. and Poggio, T. (1979). A computational theory of human stereo-vision. Proc. R. Soc. London 204, 301±328. O'Shea, R. P., Sims, A. J. H. and Govan, D. G. (1997). The eects of spatial frequency and ®eld size on spread of exclusive visibility in binocular rivalry. Vision Res. 37, 175±183. Quiang, N. and Zhu, Y. (1997). Physiological computation of binocular disparity. Vision Res. 37, 1811±1827.
Wade, N. J. (1973). Binocular rivalry and binocular fusion of afterimages. Vision Res. 13, 999±1000. Wade, N. J. (1974). The eect of orientation in binocular contour rivalry of real images and afterimages. Perception and Psychophysics 15, 227±232. Wade, N. J. (1977). Binocular rivalry between afterimages illuminated intermittently. Vision Res. 17, 310±312. Wandel, B. A. (1995). Foundations of Vision, Sinauer Associates, Sunderland, MA, USA, pp. 195±245.
PII: S0275-5408(99)00016-2
Research Note Visual perception of the Moire effect Pedro MunÄoz and Javier Alda  ptica, Universidad Complutense de Madrid, Escuela Universitaria de O  ptica, Departamento de O Avda, Arcos de JaloÂn s/n, 28037, Madrid, Spain Summary The perception of Moire fringes is studied with two different tests for binocular and monocular conditions. The results are negative for binocular conditions, and positive for the monocular case when afterimages are used. # 1999 The College of Optometrists. Published by Elsevier Science Ltd. All rights reserved
Introduction
Moire fringes are obtained any time two periodic signals are superimposed multiplicatively (in opposition to interference where the superposition is made additively). In optics, the Moire eect can be observed by placing together two similar periodical transmittances. The total transmittance is obtained by multiplying the individual ones. When the transmittances are superimposed almost in the same conditions the total transmittance shows a periodic variation whose orientation, pitch, and shape depends on the relative orientation, pitch and shape of the individual transmittances. The general treatment and some applications of the Moire eect are extensively reported in several books and papers (Kafri and Glatt, 1990; Creath and Wyant, 1992 and references therein). In the research reported here two identical square gratings were used. They were rotated with a small angle between them. This particular case allows a simpler treatment than the general one. The Moire fringes are observed oriented parallel to the bisectrix of the angle between the gratings. The period of the Moire fringes, pMoire is p , related with the period of the gratings as, pMoire 2sina where 2a is the angle between the gratings, and p the spatial period of the individual gratings. The perception of gratings in binocular conditions has been studied previously by several authors. Some previous works have been reported using two periodic gratings with a relative orientation of 908 (Wade, 1974; O'Shea et al., 1997). These papers studied the relation between rivalry, fusion, and stereopsis. Our case is
The study and development of an accurate algorithm to model the binocular function constitutes a challenging task for many researchers. As part of the binocular vision, the stereopsis function has been described as a non linear function of the signals representing the images of both eyes (Marr and Poggio, 1979). Several models have been developed to describe correspondence areas, rivalry, suppression, dominance, fusion, along with their thresholds to trigger a given perception (Quiang and Zhu, 1997; and references therein). Some models use correlations and multiplicative terms between the left and right eye images. Jenkin and Jepson (1998) propose a local phase function obtained from the multiplication of the two images to describe the binocular disparity. This function resembles closely the formalism that describes the Moire eect (Creath and Wyant, 1992). In this case the Moire based experiments would be a tool used to understand how those processes work. Our paper tries to contribute to this topic with a couple of basic experimental tests based on the Moire eect. Correspondence and reprints requests to: Dr J. Alda, University of Central Florida, School of Optics, PO Box 162700, Orlando, FL 32816-2700, USA. Tel.: +34-91-394-6874; fax: +34-91-394-6885, email: j.alda@®s.ucm.es Received: 20 May 1998 Revised form: 4 January 1999 Accepted: 2 February 1999
427
428
Ophthal. Physiol. Opt. 1999 19: No 5
rather dierent. We are looking for the perception of the Moire eect that should be perceived when the gratings are oriented almost parallel and the perception is sensitive to some multiplicative term between monocular images. Our ®rst trials were in binocular conditions. We presented to each eye two identical gratings with a relative orientation able to induce the Moire eect if the perception process is able to handle both images in the proper way. In the experiment the results were all negative. We also carried out a second experiment that used a single grating presented monocularly. The grating was used to evoke an afterimage that was superimposed with the real image of the same grating slightly rotated. In this case our objective was to ®nd out the monocular perception of Moire fringes with afterimages. Afterimages of square gratings were used in the past to override the rivalry mechanism and produce fusion of two very dierent objects. Again, the Wade experiment (Wade, 1973, 1977) was quite dierent to ours because he used afterimages in binocular conditions. With this second experiment we could demonstrate the perception of Moire fringes in monocular conditions: all the observers perceived the Moire fringes.
Materials and methods The gratings were generated by using a postscript code in a laser printer with a resolution of 600 600 dots per inch. To obtain a transmissivity grating the printing was done on an acetate transparency. In the case of re¯ectivity gratings the printing was on regular white paper. The gratings obtained were square shaped with three spatial periods. These three spatial periods correspond with three angular frequencies that are presented in Table 1 (a set of angular frequencies for each experiment). The transmittance gratings were ®xed with two square glass windows to ®t the space given by the holder of a sinoptophor. The sinoptophor was used in the binocular test. The observers were chosen once some selective tests were made. The visual accuity, after compensation of ametropies, was 1.00 or better. The binocular function and the fusion were also tested by means of typical
superposition tests using the sinoptophor. After this, a group of 28 people were selected. They were second and third year students of the School of Optics of Madrid, with ages ranging between 20 and 25 years. There were 12 male and 16 female. Before the test, we showed them what the Moire eect looked like and what the test was that we were conducting. Test of binocular fusion of gratings The objective of this test was to know if some multiplicative terms were perceived in a binocular scene (Foley, 1991; Jenkin and Jepson, 1988; Quiang and Zhu, 1997; Wandel, 1995). Two identical transmissivity gratings were placed in the arms of the sinoptophor and rotated to each other in order to achieve an angle, 2a, able to generate four or ®ve Moire fringes in the ®eld of view (see Table 1). The gratings were placed neither in horizontal nor in vertical orientation in order to avoid any preferential orientation of the perception (Wade, 1974; Kitterle and Thomas, 1980). The patterns were presented haploscopically, focused at in®nity, with a subtended angle of 58 that assured a foveal vision. The gratings were presented in photopic conditions for 20 to 25 sec. During the ®rst 10 sec the observer had to see the gratings, and during the second half of the observation he/she should explain what he/ she was perceiving. After the test, they were asked to draw a scheme of what they perceived. The test was carried out three or four times for each observer. Monocular test based on afterimages After the negative result obtained in the previous test we developed another one using afterimages. The same group of observers were trained to recognize the postimages and become familiar with their appearance. In order to improve the contrast of the black and white areas of the gratings, a set of diuse re¯ective patterns were printed on white paper having a size of 15.2 15.2 cm2 with the same spatial periods presented in Table 1. The observer was placed staring with only one eye (the other is obtured) at the middle of the test at a distance of about 40 cm. These near ®eld con-
Table 1. Spatial and angular frequencies of the tests p2 Dp (cm)
a (deg)
Angular frequency binocular test (cycle/deg)
Angular frequency monocular test (cycle/deg)
0.292 0.01 0.212 0.02 0.142 0.03
138 108 78
2.2 2.9 4.2
2.4 3.3 5.0
p and Dp are the spatial period and the error of it. a represents the angle between gratings that it is necessary to set in the sinoptophor to get the desired Moire fringes. The angular frequencies for each one of the tests is calculated for each one of the gratings
Visual perception of the Moire effect: P. MunÄoz and J. Alda
429
the dierent groups is uncorrelated with age, sex, or ametropy. For the monocular test with afterimages the results were all positive, 100% of the observers reported the vision of the Moire fringes with the three spatial frequencies gratings.
Discussion
Figure 1. Distribution of the observers with respect to the perceived effect. Along with the distribution two insets of what the observers reported are presented, (a) and (b). The partial suppression inset (b) tries to show how different areas of the visual field behave in a different form. The symmetry and location of these areas changed from one individual to another and the inset only tries to schematize the perceived scene in a very simple way.
ditions assured that the foveal area was over®lled with a test extending over a 208 angle. Then a ¯ash lamp was triggered to evoke the postimage. Immediately the test was rotated by an approximate angle of 38 or 48. After this the observer is asked to describe what he/ she is perceiving. Before the ¯ash the room was under mesopic condition and it was switched to photopic condition after the ¯ash.
Results For the test of binocular fusion of gratings the results were negative in all individuals and none perceived the Moire fringes. Twelve observers said that the gratings were perceived alternating the right and left eye images showing a temporal evolution of their dominance±suppression eects for each eye. Thirteen observers perceived a mixed scene with spatial alternate suppression areas where one of the eyes dominates the perception. The distribution of these areas was dierent for each individual (see inset (b) of Figure 1 where we have shown a schematic representation of the results. The actual perception was more irregular in shape and location). Only two observers, who also presented a remarkable ocular dominance, perceived only the grating of his/her predominant eye, and only that part of the other grating not obscured by the dominant eye could be seen by the non dominant eye (see inset (a) of Figure 1). One of the observers was unable to describe what he was perceiving in the repeated trials. The distribution of people among
Within our experimental conditions the negative results in the binocular test show that rivalry between the images of both eyes has precluded the perception of the Moire eect. Although Moire fringes were not observed, the disparity itself could be evaluated by a multiplicative term (Jenkin and Jepson, 1988), whose phase triggers the suppression±dominance eects and avoids fusion. Therefore, our results conclude that multiplicative terms of both images were not perceived. So, if they are used in the binocular function they would be processed in a ®rst stage of the algorithm, to provide a given signal for enabling or disabling the fusion between both eyes. The positive results in the afterimages monocular test can be interpreted in the retinian level. The afterimage produces a saturation with a periodic spatial structure in the photoreceptor mosaic. Then, when a similar periodic stimulus is presented, the irradiance distribution in the retina is detected by a spatially periodic function in a multiplicative way, showing the characteristic Moire pattern. Acknowledgements The authors are very grateful to the 28 students of the School of Optics who participated in the trial. We also appreciate very much the helpful discussions with Dr. Jose Alonso and Dr. Cinta Puell during the time this paper was written.
References Creath, K. and Wyant, J. C. (1992). Moire and fringe projection techniques. ed. D. Malacara. In: Optical Shop Testing, John Wiley and Sons, New York, NY, USA, pp. 653±686. Foley, J. M. (1991). Binocular Space Perception. ed. D. Rega. In: Binocular Vision, CRC Press, Boca RatoÂn, FL, USA, pp. 75±92. Jenkin, M. R. M. and Jepson, A. D. (1988). The measurement of binocular disparity. ed. Z. W. Pylyshyn. In: Computational Processes in Human Vision, Ablex Publishing Corp., Norwood, NJ, USA, pp. 69±98. Kafri, O. and Glatt, I. (1990). The Physics of Moire Metrology, John Wiley and Sons, New York, NY, USA. Kitterle, F. L. and Thomas, J. (1980). The eects of spatial frequency, orientation, and color upon binocular rivalry
430
Ophthal. Physiol. Opt. 1999 19: No 5
and monocular pattern alternation. Bulletin of the Psychonomic Society 16, 406±407. Marr, D. and Poggio, T. (1979). A computational theory of human stereo-vision. Proc. R. Soc. London 204, 301±328. O'Shea, R. P., Sims, A. J. H. and Govan, D. G. (1997). The eects of spatial frequency and ®eld size on spread of exclusive visibility in binocular rivalry. Vision Res. 37, 175±183. Quiang, N. and Zhu, Y. (1997). Physiological computation of binocular disparity. Vision Res. 37, 1811±1827.
Wade, N. J. (1973). Binocular rivalry and binocular fusion of afterimages. Vision Res. 13, 999±1000. Wade, N. J. (1974). The eect of orientation in binocular contour rivalry of real images and afterimages. Perception and Psychophysics 15, 227±232. Wade, N. J. (1977). Binocular rivalry between afterimages illuminated intermittently. Vision Res. 17, 310±312. Wandel, B. A. (1995). Foundations of Vision, Sinauer Associates, Sunderland, MA, USA, pp. 195±245.