# control of accommodative and vergence demand with mirror stereoscope

I am setting up a mirror stereoscope for use in psychophysical experiments. The stereoscope will be composed of two beamsplitters equidistant from two computer displays, with the participant sitting in front of the two beamsplitters. I am unsure how to characterize the optical properties of the stereoscope; a picture of the set-up and illustrations of my questions are in the attached image.

A. How do I compute theta, the angular subtense of the display as seen by either eye? Where is the image created?

The next two questions may be ill-posed / illustrations may be incorrect because they depend on where the image is formed.

B. Is the accommodative demand (1 / viewing distance) determined through considering the entire light path (i.e., a + b)? Relatedly, is the demand the same at each point on the mirror because a covaries with b?

C. Vergence demand is created when the lines of sight of both eyes are not parallel with infinity (e.g., lines of sight directed at the dark circle). How do I compute this demand for the image created by the mirrors? What does it mean for the lines of sight to 'not be parallel' with the emergent light?

Think that is a good start for now. Thanks.

Mirrors have a wonderfully simple rule for the images they form:

$$s = s'$$

This is stated as the (virtual) image of a mirror is an equal distance behind the mirror surface as the object is in front. Or put another way, mirrors take $$x \rightarrow -x$$ if x is the direction perpendicular to the mirror. For your example:

Since $$B = B'$$, the angular size of the display is: $$\alpha = \tan^{-1}(\frac{L}{A+B})$$ where $$L$$ is the dimension of the display, $$A$$ is the distance from the observer to the mirror, and $$B$$ is the distance of the display to the mirror.
In other words, it is exactly as if the display was in front of your.

As for your other questions, I'm unsure what you are talking about. I assume you can figure the rest out from the above facts.

• This is excellent. I'll get to crunching some of the numbers. Thank you. – Kevin May 16 '18 at 20:53
• This is a clarification of the third question. In patients with 'eye turns', the eye is no longer directed towards the object of interest-- it is rotated about a given angle either outwards or inwards. Devices such as the major amblyoscope circumvent this limitation through presenting images to the deviated eye in a mirror stereoscope as above. How is this accomplished optically? It seems like both a rotation and translation of the display-mirror system is necessary (solid black lines with arrows in image below). i.stack.imgur.com/3CWkt.png – Kevin May 16 '18 at 21:21