Hello Chandan,

If the design is done in the forward as-used direction, then the eye relief is the distance from the last surface to the exit pupil position. The merit function operand  EXPP can be used to target the exit pupil to a certain distance from the image plane, which can be used to set this distance. (EXPD can target the exit pupil diameter.)

However, it is very common to design such systems in reverse. For example consider an 8x30 binocular with an 8.3 degree full field of view and a specified eye relief of 15.1mm. In the attached ZAR the design is executed in reverse. Since the magnification is 8x, the field of view is 8.3 x 8  for a 33.2 degree maximum field angle. The exit pupil is 30mm / 8 for a 1.875mm semi-diameter.

The exit pupil diameter and the eye relief are enforced by making the exit pupil an external stop in the reversed design. This is surface 2, and the semi-diameter is fixed at 1.875 and the thickness fixed at 15.1.

For simplicity, the eyepiece and objective are modeled as paraxial lenses. The design is afocal in object and image space. No image erecting is used. (No prism.)

The implementation consists of:

1. Object at infinity with ray angle fields



2. Surface 1 just to illustrate inbound rays



3. Surface 2 as the fixed stop which defines the exit pupil and eye relief of the non-reversed system



4. Surface 3 as a paraxial lens for the eyepiece



5. Surface 4 as the field stop. Its position is determine by marginal ray height = 0 solve. It is a real image plane.



6. Surface 5 as a paraxial lens for the objective



7. The distance to the image plane is unimportant -- just for illustration

For variables:

1. The thickness from the field stop to the objective



2. The focal lengths of the eyepiece and the objective

The Merit Function Wizard is used to generate operands to minimize angular spot sizes. A few additional operands provide sufficient constraints to determine the design:

1. Angular magnification (AMAG) is targeted at -0.125 (1/8x)



2. The objective semi-diameter is allowed to float, but a Real Ray Height (REAY) operand targets its semi-diameter at 15mm

Optimization determines the values of the variables. The resulting angular spot radii are zero, which is to be expected with the paraxial lenses. (Too bad we can't buy those.)

Kind regards,

David

And here is a example in which the design is not reversed and the exit pupil desired position and eye relief are achieved by the use of merit function operands.

In this case, the objective is the aperture stop. As before, the field stop is located at a dummy surface by means of a marginal ray height = 0 solve on the preceding thickness, and the variables are the objective to eyepiece separation and the two focal lengths.

Following the eyepiece lens, there is a 15.1mm thickness  followed by a dummy (surface 5) where the exit pupil should be located. Following that there is a 10mm thickness to the image plane so we can see the ray bundles passing through the exit pupil.

Surface 5 is targeted to be the exit pupil by either or both of two operands in the merit function. An EXPP operand targets the exit pupil position to be 10mm in front of the image plane, which coincides with surface 5. An REAY operand targets that the chief ray height be zero on surface 5. Either of these by itself is able to position the exit pupil at the location of surface 5.

Kind regards,

David