The effect of dot size in random-dot stereograms on the results of stereoacuity measurements

Random-dot stereograms (RDS) are widely used in the clinical evaluation of stereopsis. The advantage of this technique is that it eliminates monocular clues more thoroughly than contour based stereo tests. In clinical practice, the stereopsis to detect contour-based stereo target, e.g. the circle pattern in the Fly Stereo Acuity Test (Vision Assessment Corporation, Illinois, USA), is considered as ‘local’, while the stereopsis to detect random dot-based stereo target, e.g. the Pacman hidden in TNO stereotest (Lameris Ootech BV, Ede, Netherlands), is considered as ‘global’ [1]. The neural processing of ‘local’ and ‘global’ stereopsis may be different. However, the two mechanisms cannot be entirely separated [2]. In neurophysiology research, local and global stereograms may be determined by the number of dots contained within the stereogram. For example, ‘Local’ stereopsis is traditionally defined by the use of a small number of dots to form a pattern, while ‘global’ stereopsis involves the use of many dots to form a pattern. From this point of view, a test pattern consists of a small number of random dots and may also be considered ‘local’ [3]. In Gantz’s research, the density of RDSs lower than 0.39% was considered a ‘local’ stereo target; otherwise, it was considered a ‘global’ stereo target [4].

In the Frisby stereotest (Stereotest Ltd., Sheffield, UK) [1, 5], the subject is asked to identify a shape hidden in an array of randomly arranged triangles of varying sizes. The shape is distinguished by a real difference in depth and can be perceived without the help of any other appliance. In the random-dot E stereo test (Vision Assessment Corporation, Illinois, USA) [1, 5], the letter E is hidden in a random dot array, but can be perceived with the aid of polarising spectacles that divide the images seen by the two eyes. In the TNO test [1, 5], the test shapes are disks with a missing sector and the two stereo elements printed in red and green for viewing with red/green anaglyph stereo glasses. Although the measurements are all based on detecting the minimum disparities a subject is able to distinguish, the test result evaluated with different stereotests may differ from each other [6]: For example, the stereoacuity measured with the TNO test is worse than the acuity measured with other methods, either in a normal population [7] or in patients with abnormal binocular vision [8]. The mechanisms underlying these differences have not been clearly established [9].

Several researchers have discussed whether dot size in a RDS could affect the test result. In Henriksen’s study, the size of half-matched RDSs (half the dots in RDSs are correlated and half are anticorrelated) was set at 0.025°, 0.05° and 0.075° respectively. They found that psychophysical performance decreases with smaller dot size, and stated that smaller dots might decrease the local correlation variability [10]. A previous study has confirmed that increasing dot size may improve accuracy in detecting binocular disparity - slightly, but significantly [11].

Whatever the test symbol or the test procedure, the RDSs used in the clinic are simpler than those conducted in a laboratory environment. We adopted our newly designed stereoacuity measurement system, a phoropter combined with two 4 K smartphones [12], to explore the effect of dot size in RDS. Extremely small dots, far smaller than the recognition resolution of the human eye, were utilized. For some stereotests, e.g. Random dot E test, the examined distance could be prolonged to obtain a finer stereo threshold. The visual angle of the dots in the background may reduce to an unrecognizable level. The aim of this study was to evaluate the possible difference of stereopsis tested with RDSs composed of different dot sizes.

The random-dot stereogram is the most used method of evaluating stereoacuity. Several tests widely used in research or the clinic are based on this technique. Different designs of the test shapes, or differences in the random dots, may lead to differences in the results of each method. In Simon’s view, the poorer stereoacuity measured by the Frisby test may be caused by the widely spaced random elements that make the contour of the stereofigure discontiguous with the surrounding pattern [14]. Gantz and Bedell found that the effect of dot density on stereothresholds was significant [4]. However, dot size is another factor that may affect the test result [3, 11]. Forty years ago, Pitblado studied cerebral asymmetry with the aid of RDS. For the recognition of cyclopean shapes, left visual field (right hemisphere) superiority was observed when the stereogram was comprised of small dots; with large dots, performance was better in the right visual field (left hemisphere). The study also showed that increasing the dot size in the random background could slightly, but significantly, enhance distinguishment accuracy with smaller binocular disparity [11]. Henriksen adopted a stereogram named half-matched to detect the stereo threshold. The research showed that large dots produced stronger responses than small dots, and psychophysical performance decreased with smaller dot size [10].

For the most part, the smallest dot size in RDSs of previous literature was larger than normal recognizability (Snellen VA) of 1 min arc, such as 2.2 min arc in Gray’s study [15], 1.8 × 2.7 in min arc in Ito’s study [16], 3.5 min arc in Tortter’s research [17], and 5 min arc in Stevenson’ work [18], etc.. In our experiment, the smallest dot, 1 × 1 px, with the visual angle of 0.17 min arc, was far smaller than recognition resolution of a normal subject. The test result of RDSs composed of extremely small dots was significantly lower than those composed with larger dots. Blur may be one of the reasons. Recognizability is a measurement of the resolution power of the eye to distinguish adjacent points [19]. Assume that two 1 × 1 px black dots are separated by a 1 × 1 px white dot, if an observer can distinguish between these two black dots, his/her VA should not be lower than 0.17 min arc. However, this resolution could not actually be achieved by a normal eye. A subject with normal VA (about 1 min arc) cannot make out these two dots, but may see only one blurred dot. Under this circumstance, the background composed of extremely small random dots may be expressed as a mottled grey background. The blurred retinal image reduces local contrast and the decreased contrast causes a decrement in stereoacuity [20‐22]. Schmidt [23] induced blur with the aid of lenses and found stereoacuity deteriorated 1.341 times faster than Snellen acuity tested under binocular blur conditions and 3.77 times faster under the monocular blur. Crowding may be another factor to influence the test result. The minimum separation from adjacent elements, 1 min arc or more could avoid crowding [24]. Obviously, 0.17 min arc (1 px interval) is too small.

The stereopsis measurements carried out in the clinic are not as complicated as those utilized in a laboratory environment. The test patterns are relatively simple and the target symbols are easy to distinguish. After all, young children should not be excluded from the tests. The RDSs used in the clinic vary by dot size, density and shape. Piano et al. [25] studied 5 commonly used RDSs in the clinic and found a significant difference existing between TNO and Frisby stereotests. It is unwise to attempt to use stereotests interchangeably to test subjects.

In our test, eight RDSs were all carried out in the clinic (Table 1). The dot size at 40 cm was greater than or equal to 1 min arc in 6 out of 8 RDSs, while the dot size was close to 1 min arc (0.8 min arc) in the other 2 RDSs. The test result may be affected by reducing the dot size while increasing the test distance. An RDS composed of extremely small dots may underestimate the stereo threshold according to our experiment. However, there was no significant difference in stereopsis when evaluating stereoacuity with two different dot sizes (6-px versus 10-px). This consequence was different from the literature mentioned above. The discrepancy may result from the different test pattern designs, different test procedures, and different test environments. This reminds us, whether designing or using RDS to test stereopsis, the smallest dot size in the background should be larger than standard subject recognizability at test distance. Otherwise, underestimation of stereo threshold may result. Nevertheless, larger dot size is not necessarily better. Monocular clues become obvious with larger dots because the outline of the target symbol tends to be discerned in this circumstance.

The limitation of our study is that the participants recruited were in a relatively narrow age range, which may lead to possible age bias. All of them were young doctors, nurses and students from our department. Another limitation was that the relative influence factors, such as dot density, were not included in the study. More thorough research should be conducted in future.

Although disparities in stereotarget settings of a RDS are the test unit used to evaluate the stereothreshold, the effect of background dot sizes should not be neglected. It is recommended to avoid adopting random dot sizes that are smaller than the recognizability of the subject. Otherwise, doing so would result in the underestimation of stereothreshold.