Double Gauss Lens Image Simulation

If a lens has designed for an imaging application, it is useful to simulate the image that a user would expect see. In this tutorial we demonstrate how to load a bitmap that can be used as the object in a finite conjugate ray trace.

Model Definition

The model used in this simulation is the Double Gauss Lens found in the Ray Optics Module Application Libraries. The lens shown in Figure 1 is a 100 mm focal length lens by Lautebacher & Brendel (see Ref. 1). Full details of this model (including instructions for creating the lens geometry) can be found in the Double Gauss Lens tutorial.

Figure 1: The Double Gauss Lens geometry sequence. Details of this lens are from Ref. 1.

Study 1

The lens, which has an f/1.7 focal ratio and a 19° field of view, has a focal plane which is positioned for imaging an object at infinity. In this model we will place the bitmap at a distance of 1 meter in front of the lens. is therefore used to determine the new finite conjugate focal plane.

We do this by releasing a cone of rays from the point on the optical axis intersecting the object plane. The rays can be made to ignore the image surface because, as can be seen in the Ray Diagram shown in Figure 2, the focus is now somewhere behind this plane.

The Spot Diagram feature can be used to automatically find the location of the best RMS focus (see Figure 3). The on-axis aberrations can also be seen in Figure 4. For more details see the Modeling Instructions at the end of this document.

Figure 2: A ray diagram showing the finite conjugate ray trace. The rays now pas through the nominal focal plane.

Figure 3: A spot diagram showing the global coordinates of the finite conjugate focal plane.

Figure 4: The aberration plot showing the wavefront error at the new focus. The left diagram includes all Zernike terms, whereas the right diagram does not include piston and defocus.

Study 2

The image simulation is performed using . First, the geometry is updated to locate the image plane at the new focus. In this simulation only a small section of the object surface will be sampled. Therefore, the geometry now includes rectangular surfaces on both the object and image planes (see Figure 5). These are approximately scaled so that an object (the bitmap) placed on the object surface will be imaged onto the section of the image plane defined by the image surface.

The is used to define the spatial sampling of the rays that are released from the object surface, and the spatial binning of rays on the image surface. A mesh with a set to have a fixed number of elements is applied to each of the object and image surfaces. The number of elements is npix on the image surface and 2*npix on the object surface.

The rays used in this simulation are defined using a feature. The spatial density of these rays as they are released from the object surface is proportional to the value of the imported bitmap. Each ray is released into a solid angle approximately centered on the entrance pupil of the lens. A random sampling from within this cone gives a uniform distribution of rays across the entrance pupil.

Detailed step-by-step instructions can be found in the Modeling Instructions.

Figure 5: The Double Gauss Lens Image Simulation geometry. The object surface is on the left.

Results and Discussion

A simulation using 100,000 rays is shown in Figure 6 and Figure 7. Figure 8 shows the 2D image side by side with the original bitmap object.

Figure 6: Ray diagram showing the object and image surfaces together with a fraction of the rays used in this simulation.

Figure 7: A closeup of the image simulation ray diagram.

Figure 8: The object (left) and the resulting ray traced image (right).

Reference

1. W.J. Smith, Modern lens design, vol. 2. New York, NY, USA: McGraw-Hill, 2005.

Ray_Optics_Module/Lenses_Cameras_and_Telescopes/double_gauss_lens_image_simulation

Modeling Instructions

Application Libraries

From the menu, choose .

In the window, select in the tree.

Click

Component 1 (comp1)

For this simulation the diameter of the aperture stop is slightly reduced. This will slightly improve the image quality at the finite conjugate focus.

In the window, expand the node.

Double Gauss Lens

Stop (pi4)

In the window, expand the node, then click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
d1	0.80*d1_S	29.76 mm	Diameter, inner

Geometrical Optics (gop)

Use the following steps to determine the distance to the finite conjugate focal plane.

Release from Grid 2

In the window, under right-click and choose . This will be used to release rays from the object plane.

In the window for , locate the section.

In the qz,0 text field, type -1[m].

Locate the section. From the list, choose .

From the list, choose .

In the Nθ text field, type N_ring.

Specify the r vector as


nix	x
niy	y
niz	z

This is the direction of the optical axis.

In the α text field, type 0.70*atan(0.5*d1_clear_1/1[m]). This is the approximate angular size of the Double Gauss Lens entrance pupil as seen from the object plane.

Study 1

Next, adjust the study to allow for the finite conjugate ray trace.

Step 1: Ray Tracing

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type 0 1200. The maximum optical path length now accounts for the distance to the object plane.

Locate the section. Select the check box.

In the tree, select and .

Right-click and choose . This disables the original (infinite conjugate) release. It also allows the rays to pass through the image plane which needs to be repositioned.

In the toolbar, click

Results

First, update the ray diagram to show the finite conjugate ray trace.

Ray Diagram 1

In the window for , locate the section.

Clear the check box.

Click

In the toolbar, click

Click the

button in the toolbar. Compare the result to Figure 2.

Spot Diagram

We now use the Spot Diagram feature to compute the new focus position.

In the window, click .

In the window for , locate the section.

From the list, choose .

Click

Spot Diagram 1

In the window, expand the node.

Right-click and choose . This spot diagram is no longer used in this modified study.

Spot Diagram 2

This spot diagram uses an Intersection Point Dataset.

In the window, click .

In the window for , click to expand the section.

From the list, choose .

Click to expand the section. Click . The Intersection Point Dataset will be repositioned to minimize the RMS spot size.

Color Expression 1

In the window, click .

In the window for , locate the section.

In the text field, type at(0,gop.phic).

In the toolbar, click

. The global coordinates this location can be now be seen in this plot. Compare the result to Figure 3.

Optical Aberration Diagram

Update the Optical Aberration Diagram to show the aberrations with the adjusted focus.

In the window, under click .

In the window for , click

Optical Aberration 1

In the window, click .

In the window for , locate the section.

Click . This will also reposition this dataset at the location that minimizes the RMS spot size. Compare the result to Figure 4.

Global Definitions

Add a new parameters node containing details of the image simulation. A parameter defining the distance to the finite conjugate focal plane location is entered here. The total number of rays to use in the image simulation (Nrays) is also defined here.

Parameters 3: Image Simulation

In the toolbar, click

and choose .

In the window for , type Parameters 3: Image Simulation in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Value	Description
h_object	400.0[mm]	0.4 m	Object height
mag	9.5	9.5	Approximate maginifcation
h_image	h_object/mag	0.042105 m	Image height
Z_focus	147.124[mm]	0.14712 m	Finite conjugate focus
Nrays	250e3	2.5E5	Total number of rays
npix	300	300	Number of image pixels

In the following steps we add the object plane and update the location and size of the image plane.

In the window, under right-click and choose .

Part Libraries

In the window, select in the tree.

Click

Double Gauss Lens

Image (pi8)

In the window, under click .

In the window for , locate the section.

From the list, choose . This will convert the image plane from circular to rectangular.

Locate the section. In the table, enter the following settings:


Name	Expression	Value	Description
w0	h_image	42.105 mm	Width, outer
h0	h_image	42.105 mm	Height, outer
w1	0	0 m	Width, inner
h1	0	0 m	Height, inner

Locate the section. Find the subsection. From the list, choose .

From the list, choose .

Find the subsection. In the text field, type Z_focus. This is the z-component of the best focus position.

Object

In the toolbar, click

and choose . This plane will to position the object (an imported bitmap) in this simulation.

In the window for , type Object in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Value	Description
w0	h_object	400 mm	Width, outer
h0	h_object	400 mm	Height, outer
w1	0	0 m	Width, inner
h1	0	0 m	Height, inner

Locate the section. Find the subsection. From the list, choose .

From the list, choose .

Find the subsection. In the text field, type -1[m].

Click to expand the section. Click to select row number 1 in the table.

Click .

In the dialog box, type Object Plane in the text field.

Click .

In the window for , click

. The new geometry for this model can be seen in Figure 5.

Mesh 1

Details of the mesh need to be defined to support the image simulation.

Size 1

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. Click the button.

Locate the section. Select the check box.

In the associated text field, type 1.0.

Size

In the window, click .

In the window for , locate the section.

From the list, choose . It is necessary to increase the level of the Physics-based mesh refinement to account for the increase in size of the model geometry.

Mapped 1

In the toolbar, click

and choose . A mapped mesh will be used to define the spatial bins for releasing rays from the object, and for accumulating the image.

In the window for , locate the section.

From the list, choose .

Distribution 1

Right-click and choose .

Select Edges 1–3 and 160 only.

In the window for , locate the section.

In the text field, type 2*npix. This ensures that there are approximately two mesh elements (in each direction) on the object plane for each image mesh element.

Mapped 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Distribution 1

Right-click and choose .

Select Edges 54–56 and 150 only.

In the window for , locate the section.

In the text field, type npix.

Free Tetrahedral 1

In the toolbar, click

In the window for , click

Definitions

In this section we load a bitmap to use as the object in this simulation.

Image 1 (im1)

In the toolbar, click

and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file double_gauss_lens_image_simulation_example.png.

Locate the section. In the text field, type -h_object/2.

In the text field, type h_object/2.

In the text field, type -h_object/2.

In the text field, type h_object/2.

Locate the section. Click

Geometrical Optics (gop)

Here we add a release to launch rays based on the imported bitmap.

Release from Boundary 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose . This is the Boundary Selection referenced in the geometry Part Instance that defines the object plane.

Locate the section. From the list, choose .

In the N text field, type Nrays.

In the ρ text field, type comp1.im1(x,y). The number density of the rays launched from the object plane will be proportional to the value of the image at each launch location.