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Keck Telescope
Introduction
The Keck Telescope is a 10 meter diameter telescope with a Ritchey-Chrétien optical design. It is noted for being one of the first large optical telescopes to utilize a light weight segmented primary mirror. This tutorial demonstrates how to use the Conic Polygonal Mirror Off Axis 3D part from the Part Library to construct a model of the Keck Telescope segmented primary mirror. An overview of the Keck Telescope is shown in Figure 1.
Figure 1: Overview of the Keck Telescope.
Model Definition
Details of the Keck Telescope can be found in Ref. 1 and Ref. 2. A summary of the parameters used in this tutorial is given in Table 1. The resulting Keck Telescope geometry sequence is shown in Figure 2.
The telescope primary mirror geometry is constructed using instances of the Conic Polygonal Mirror Off Axis 3D from the Ray Optics Part Library. It consists of 36 hexagonal segments with a common parent surface. These mirrors are arranged in a “four-ring” geometry (i.e., with a missing central segment). There are 6 unique mirrors, each of which is replicated 6 times in a 6-fold rotational pattern. Details of the primary mirror segments are given in Table 2. The geometry of the first 6 mirrors can be seen in Figure 3 and in Figure 4 the complete primary mirror geometry can be seen.
The Conic Mirror On Axis 3D and Elliptical Planar Mirror 3D parts are used to create the secondary and tertiary mirrors respectively. The curved image surface is defined using a Parametric Surface primitive.
λvac
550 nm
θx,i
Nominal x field angle, field i = 1,2,3
θy,i
Nominal y field angle, field i = 1,2,3
Nring
20
Pnom
10.949 m
Rprim
-35.00000 m
kprim
-1.0037963
d0,prim
1.79 m
Tc,prim
75.0 mm
Zprim
0 m
Rsec
4.849338 m
ksec
-1.6430812
d0,sec
1.429 m
Tc,sec
150.0 mm
Zsec
-15.35821 m
d0,ter
0.873 m
θter
45.0°
Zter
-4.0 m
dimg
0.873 m
Cimg
0.471 m1
Zimg
-7.0 m
 
 
Figure 2: The Keck Telescope geometry sequence.
Figure 3: The 6 common off axis mirror segments. Each of the unique mirrors has been assigned a different color. The central (on axis) mirror is not used.
Figure 4: The complete primary mirror. The outline of the set of 6 common mirrors is shown in black.
Results and Discussion
A ray trace has been performed at a single wavelength (550 nm) at three field angles (0, 2.5 and 5 arcminutes). Figure 5 shows the resulting ray trajectories; the Color Expression represents the ray positions on the image surface.
In Figure 6 the intersection of the rays with the image surface is shown. This spot diagram shows each of the three field angles, where the Color Expression is the initial radial location at the entrance pupil.
Figure 5: Ray diagram of the Keck Telescope colored by radial distance from the centroid.
References
1. J. E. Nelson, T. S. Mast, Optical Design and Instrumentation of the Keck Observatory, Proc. SPIE 0628, 1986.
2. J. E. Nelson, T. S. Mast, S. M. Faber (editors), The Design of the Keck Observatory and Telescope, Keck Observatory Report No. 90, 1985.
 
Figure 6: Spot diagram of the Keck Telescope colored by radial distance from the center of the entrance pupil.
Application Library path: Ray_Optics_Module/Lenses_Cameras_and_Telescopes/keck_telescope
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Optics>Ray Optics>Geometrical Optics (gop).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Ray Tracing.
6
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file keck_telescope_parameters.txt. This text file contains the prescription for the telescope (including the segmented mirror geometry) as well as study parameters.
Component 1 (comp1)
1
In the Model Builder window, click Component 1 (comp1).
2
In the Settings window for Component, locate the General section.
3
Find the Mesh frame coordinates subsection. From the Geometry shape function list, choose Quartic Lagrange. The ray tracing algorithm used by the Geometrical Optics interface computes the refracted ray direction based on a discretized geometry via the underlying finite element mesh. A quartic geometry shape order will reduce the discretization error compared to the default, which uses linear and quadratic polynomials.
Geometry 1
The Keck telescope can be constructing using several built-in parts from the Ray Optics Part Library. The Conic Polygonal Mirror Off Axis 3D part is used to create the hexagonal mirror segments, the Conic Mirror On Axis 3D part, is used for the secondary mirror, and the Elliptical Planar Mirror 3D part is used to define the tertiary mirror.
Part Libraries
1
In the Home toolbar, click  Windows and choose Part Libraries.
2
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
3
In the Part Libraries window, select Ray Optics Module>3D>Mirrors>conic_polygonal_mirror_off_axis_3d in the tree.
4
Click  Add to Geometry.
5
In the Select Part Variant dialog box, select Specify clear aperture diameter and off axis distance in the Select part variant list.
6
Geometry 1
Primary Mirror 1
To create the segmented primary mirror, begin by defining the 6 common off axis segments.
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Conic Polygonal Mirror Off Axis 3D 1 (pi1).
2
In the Settings window for Part Instance, type Primary Mirror 1 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Rotation subsection. In the Rotation angle text field, type rho1.
5
Click to expand the Boundary Selections section. Click New Cumulative Selection.
6
In the New Cumulative Selection dialog box, type Mirrors in the Name text field.
7
Click OK. This selection, and those that follow will be used later in the model setup.
8
In the Settings window for Part Instance, locate the Boundary Selections section.
9
Click New Cumulative Selection.
10
In the New Cumulative Selection dialog box, type Obstructions in the Name text field.
11
Now, apply each of these selections.
12
In the Settings window for Part Instance, locate the Boundary Selections section.
13
In the steps that follow, duplicate the first mirror and change only those settings unique to the 5 remaining common segments.
Primary Mirror 2
1
Right-click Primary Mirror 1 and choose Duplicate.
2
In the Settings window for Part Instance, type Primary Mirror 2 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Rotation subsection. In the Rotation angle text field, type rho2.
Primary Mirror 3
1
Right-click Primary Mirror 2 and choose Duplicate.
2
In the Settings window for Part Instance, type Primary Mirror 3 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Rotation subsection. In the Rotation angle text field, type rho3.
Primary Mirror 4
1
Right-click Primary Mirror 3 and choose Duplicate.
2
In the Settings window for Part Instance, type Primary Mirror 4 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Rotation subsection. In the Rotation angle text field, type rho4.
Primary Mirror 5
1
Right-click Primary Mirror 4 and choose Duplicate.
2
In the Settings window for Part Instance, type Primary Mirror 5 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Rotation subsection. In the Rotation angle text field, type rho5.
Primary Mirror 6
1
Right-click Primary Mirror 5 and choose Duplicate.
2
In the Settings window for Part Instance, type Primary Mirror 6 in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Rotation subsection. In the Rotation angle text field, type rho6.
Rotate 1 (rot1)
Now, create the segmented primary mirror by creating 6 copies of the 6 common segments. It would also be possible to create 36 unique mirror segments.
1
In the Geometry toolbar, click  Transforms and choose Rotate.
2
Click in the Graphics window and then press Ctrl+A to select all objects.
3
In the Settings window for Rotate, locate the Rotation section.
4
In the Angle text field, type range(0,60,300).
Next, add the secondary and tertiary mirrors, and define the image surface.
Part Libraries
1
In the Geometry toolbar, click  Parts and choose Part Libraries.
2
In the Model Builder window, click Geometry 1.
3
In the Part Libraries window, select Ray Optics Module>3D>Mirrors>conic_mirror_on_axis_3d in the tree.
4
Click  Add to Geometry.
5
In the Select Part Variant dialog box, select Specify clear aperture diameter in the Select part variant list.
6
Geometry 1
Secondary Mirror
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Conic Mirror On Axis 3D 1 (pi7).
2
In the Settings window for Part Instance, type Secondary Mirror in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
The extra azimuthal points are used to reduce the effects of discretization around the edge of the secondary mirror.
4
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Primary Mirror 1 (pi1).
5
From the Work plane list, choose Mirror parent vertex intersection (wp1).
6
Find the Displacement subsection. In the zw text field, type Z_sec.
7
Locate the Boundary Selections section. In the table, enter the following settings:
Part Libraries
1
In the Geometry toolbar, click  Parts and choose Part Libraries.
2
In the Model Builder window, click Geometry 1.
3
In the Part Libraries window, select Ray Optics Module>3D>Mirrors>elliptical_planar_mirror_3d in the tree.
4
Click  Add to Geometry.
5
In the Select Part Variant dialog box, select Specify mirror angle and minor axis diameter in the Select part variant list.
6
Geometry 1
Tertiary Mirror
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Elliptical Planar Mirror 3D 1 (pi8).
2
In the Settings window for Part Instance, type Tertiary Mirror in the Label text field.
3
Locate the Input Parameters section. In the table, enter the following settings:
4
Locate the Position and Orientation of Output section. Find the Coordinate system to match subsection. From the Take work plane from list, choose Primary Mirror 1 (pi1).
5
From the Work plane list, choose Mirror parent vertex intersection (wp1).
6
Find the Displacement subsection. In the zw text field, type Z_ter.
7
Locate the Boundary Selections section. In the table, enter the following settings:
Image Surface
Finally, a parametric surface is used to define the image surface.
1
In the Geometry toolbar, click  More Primitives and choose Parametric Surface.
2
In the Settings window for Parametric Surface, type Image Surface in the Label text field.
3
Locate the Parameters section. Find the First parameter subsection. In the Minimum text field, type -d_img/2.
4
In the Maximum text field, type d_img/2.
5
Find the Second parameter subsection. In the Minimum text field, type -d_img/2.
6
In the Maximum text field, type d_img/2.
7
Locate the Expressions section. In the x text field, type s1.
8
In the y text field, type s2.
9
In the z text field, type C_img*(s1^2 + s2^2)/(1 + sqrt(1 - C_img^2*(s1^2 + s2^2)))*1[m]. This is the equation of a sphere having a curvature C_img. This is the curvature defined in the Parameters node.
10
Locate the Coordinate System section. From the Take work plane from list, choose Tertiary Mirror (pi8).
11
From the Work plane list, choose Exit plane (wp4).
12
Locate the Position section. In the zw text field, type Z_img.
13
Locate the Selections of Resulting Entities section. Select the Resulting objects selection check box.
14
In the Geometry toolbar, click  Build All.
15
Click the  Go to Default View button in the Graphics toolbar.
16
Click the  Orthographic Projection button in the Graphics toolbar.
17
Click the  Zoom Extents button in the Graphics toolbar. Compare the resulting geometry to Figure 2.
Geometrical Optics (gop)
1
In the Model Builder window, under Component 1 (comp1) click Geometrical Optics (gop).
2
In the Settings window for Geometrical Optics, locate the Domain Selection section.
3
Click  Clear Selection. Only mirrors are being used in this model. Clearing the domain selection allows the model to be run without adding materials.
4
Locate the Ray Release and Propagation section. In the Maximum number of secondary rays text field, type 0. Stray light is not being traced, so reflected rays will not be produced at the lens surfaces.
5
Select the Use geometry normals for ray-boundary interactions check box. In this simulation, the geometry normals are used to apply the boundary conditions on all refracting surfaces. This is appropriate for the highest accuracy ray traces in single-physics simulations, where the geometry is not deformed.
Mirrors
1
In the Physics toolbar, click  Boundaries and choose Mirror.
2
In the Settings window for Mirror, type Mirrors in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Mirrors. This is the cumulative selection defined above.
Obstructions
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
In the Settings window for Wall, type Obstructions in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Obstructions.
4
Locate the Wall Condition section. From the Wall condition list, choose Disappear. Rays that hit any of these surfaces will be removed.
Image
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
In the Settings window for Wall, type Image in the Label text field.
3
Locate the Boundary Selection section. From the Selection list, choose Image Surface. The default wall condition Freeze will be applied to rays that reach the image surface.
Next, create release features for each of the field angles defined in the Parameters node.
Release from Grid 1
1
In the Physics toolbar, click  Global and choose Release from Grid.
2
In the Settings window for Release from Grid, locate the Initial Coordinates section.
3
From the Grid type list, choose Hexapolar.
4
Specify the qc vector as
5
Specify the rc vector as
6
In the Rc text field, type R_nom.
7
In the Nc text field, type N_ring.
8
Locate the Ray Direction Vector section. Specify the L0 vector as
Release from Grid 2
1
Right-click Release from Grid 1 and choose Duplicate.
2
In the Settings window for Release from Grid, locate the Initial Coordinates section.
3
Specify the qc vector as
4
Locate the Ray Direction Vector section. Specify the L0 vector as
Release from Grid 3
1
Right-click Release from Grid 2 and choose Duplicate.
2
In the Settings window for Release from Grid, locate the Initial Coordinates section.
3
Specify the qc vector as
4
Locate the Ray Direction Vector section. Specify the L0 vector as
Ray Termination 1
Add a ray termination feature to remove rays that are not reflected by the segmented mirror.
1
In the Physics toolbar, click  Global and choose Ray Termination.
2
In the Settings window for Ray Termination, locate the Termination Criteria section.
3
From the Spatial extents of ray propagation list, choose Bounding box, user defined.
4
In the xmin text field, type -P_nom.
5
In the xmax text field, type P_nom.
6
In the ymin text field, type -P_nom.
7
In the ymax text field, type P_nom.
8
In the zmin text field, type -1.0[m].
9
In the zmax text field, type 18.0[m].
10
Right-click Ray Termination 1 and choose Build All. The default Physics-controlled mesh is sufficient for this simulation.
Study 1
Step 1: Ray Tracing
1
In the Model Builder window, under Study 1 click Step 1: Ray Tracing.
2
In the Settings window for Ray Tracing, locate the Study Settings section.
3
From the Time-step specification list, choose Specify maximum path length.
4
In the Lengths text field, type 0 60. This path length is sufficient to ensure that all rays reach the image plane.
5
In the Home toolbar, click  Compute.
Now, create a ray diagram.
Results
Ray Diagram
1
In the Settings window for 3D Plot Group, type Ray Diagram in the Label text field.
2
Locate the Color Legend section. Select the Show units check box.
3
In the Model Builder window, expand the Ray Diagram node.
Color Expression 1
1
In the Model Builder window, expand the Results>Ray Diagram>Ray Trajectories 1 node, then click Color Expression 1.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type at('last',gop.rrel). This is the radial coordinate relative to the centroid at the image plane for each release feature.
4
From the Unit list, choose µm.
Surface 1
1
In the Model Builder window, right-click Ray Diagram and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type x^2+y^2.
4
Locate the Coloring and Style section. From the Coloring list, choose Gradient.
5
Clear the Color legend check box.
6
Select the Reverse color gradient check box.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Mirrors.
4
In the Ray Diagram toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar. Compare the resulting image to Figure 5.
Spot Diagram
Next, create a spot diagram.
1
In the Home toolbar, click  Add Plot Group and choose 2D Plot Group.
2
In the Settings window for 2D Plot Group, type Spot Diagram in the Label text field.
3
Locate the Color Legend section. Select the Show units check box.
Spot Diagram 1
1
In the Spot Diagram toolbar, click  More Plots and choose Spot Diagram. Make some adjustments to the default Spot Diagram in order to show the spot size and coordinates on the curved image surface.
2
In the Settings window for Spot Diagram, click to expand the Focal Plane Orientation section.
3
From the Transverse direction list, choose User defined.
4
In the x text field, type 0.
5
In the y text field, type 1.
6
Locate the Layout section. From the Layout list, choose Rectangular grid.
7
In the Number of columns text field, type 1.
8
In the Vertical padding factor text field, type 0.
9
Click to expand the Annotations section. Select the Show spot coordinates check box.
10
From the Coordinate system list, choose Global.
11
In the Display precision text field, type 7.
12
Select the Show circle check box.
13
In the Radius text field, type r_Airy.
14
Select the Fit annotations to spot check box.
Color Expression 1
1
Right-click Spot Diagram 1 and choose Color Expression.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type at(0,gop.rrel). This is the radial coordinate relative to the centroid at the entrance pupil for each ray release.
4
In the Spot Diagram toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar. Compare the resulting image to Figure 6.