DOE and Thin Lens Surface Overview

Diffractive Surface

With diffractive surface, you can model thin lens that corresponds to a theoretical lens.

Two possibilities are available: Thin lens or Diffractive optical element (DOE).

Note: Note that diffractive lenses are modeled by choosing the Diffractive optical element mode.

For the diffractive optical element, this surface type models the DOE effect on light.

Warning: This model can only figure simple DOEs (not complex holograms for example) like a holographic lens.

The example of a lens with a DOE on one of its face is used industrially in CD reader devices. With this you can have a simple optical system to make little focus point. The advantages are a simple mechanical structure, a low weight and a low price.

The DOEs can be used to focus on something else than a point: an ellipse for example. It is possible to replace a parabolic mirror by a plane DOE. It is possible to replace a complex optical element by a plane DOE with the right function.

Transmission

Basic Fresnel interactions for transmission trough a surface gives the following changes on photons direction (in the local surface’s base).



Ni

Material index

(li,mi,ni)

Direction vector of the ray

This direction change is modified as follows by a DOE surface:



Where f is the user defined phase function:



lo

The base wavelength at which the DOE has been designed

f

The diffractive focal of the DOE (at lo)

r²

x² + y²

bi

The radial coefficients of the polynomial

P(x,y)

The whole polygon (not with only radial coefficients)



For a reflection

Equations are:





The surface is 100% transmitting or 100% reflecting.

Warning: There is no diffused light.

If all coefficients are null, the surface acts as 100% specular simple scattering surface with reflection or transmission only.

Thin lens



With Thin lens you can focus a collimated beam without modeling a real lens.

Warning: DOE applied on a lens.

Using DOE on a Thin Lens

We can use the DOE surface model on one plane face of a lens as follows:

  1. Define a lens (with default parameters for example).

  2. Define a box with x=50 y=50 z=10 dimensions and DOE surface defined in the previous EDIT box.

  3. Make a Boolean operation: lens-box.

    You can also create a source and watch the effect of the surface on light:



    Without DOE



    With DOE

This test shows that DOE surface model can be applied on lenses with a diffractive optical element on one of its faces only.

It is possible to test some coefficients because of their simple effect:

  • We can use l = 532 nm as the base wavelength and f = 10 mm for the diffractive focal.

  • We can see that a DOE with all its bi and aij coefficients null has no effect on light.

  • We can now let b1 = -0.5 and see that a collimated beam converges on one point located 10 mm from the DOE. If b1 = 0.5 the beam diverges.

The aij coefficients are used to break the revolution symmetry:

  • If b1 = -0.5, use a10 and a01 to move the focal point in the I and/or J vectors direction.

  • If a10=d / f the focal point moves d millimeters away.

The a20 and a02 coefficients allows you to use different focal lengths on x and y-axes: -0.05 for a 10 mm length.

Thin Lens Behavior

During a raytracing simulation, for each new ray impact, the optical lens center is computed by evaluating the intersection between the optical axis and the lens plan place at ray's impact. Then the impact coordinate from the optical lens center is used for computing the emergent ray direction.

The thin lens behavior is correct if:
  • In Speos, the Thin Lens (*.doe) property is applied only on a flat face.
  • The flat face (plane) is collinear to the lens plane defined by the thin lens vectors i and j.

Simple Lens

The setup for a simple lens is:

  1. Select DOE surface.

  2. Set the base wavelength.

  3. Set the focal length of the lens.

  4. Set all coefficients to zero, except B1 = -0.5.