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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 parts from the Ray Optics Module Part Libraries 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.
Details of the primary mirror geometry described below. Instances of the Conic Mirror On Axis 3D part and the Elliptical Planar Mirror 3D part are used to create the secondary and tertiary mirrors respectively. The curved image surface is created using a Parametric Surface primitive. The full Keck Telescope geometry sequence is shown in Figure 4.
 
Table 1: Keck TELESCOPE PARAMeters.
Name
Value
Details
 λvac
 550 nm
Vacuum wavelength
 θx,i
Nominal x field angle, field i = 1,2,3
 θy,i
Nominal y field angle, field i = 1,2,3
 Nring
 20
Number of hexapolar rings
 Pnom
 10.949 m
Entrance pupil diameter
Primary mirror:
 
 Rprim
 -35.00000 m
Primary mirror radius of curvature
 kprim
 -1.0037963
Primary mirror conic constant
 d0,prim
 1.79 m
Primary mirror segment diameter
 Tc,prim
 75.0 mm
Primary mirror segment center thickness
 Zprim
 0 m
Primary mirror position
Secondary mirror:
 
 Rsec
 4.849338 m
Secondary mirror radius of curvature
 ksec
 -1.6430812
Secondary mirror conic constant
 d0,sec
 1.429 m
Secondary mirror diameter
 Tc,sec
 150.0 mm
Secondary mirror center thickness (nominal)
 Zsec
 -15.35821 m
Secondary mirror position (relative to primary vertex)
Tertiary mirror:
 
 d0,ter
 0.873 m
Tertiary mirror minor axis diameter
 θter
 45.0°
Tertiary mirror fold angle
 Zter
 -4.0 m
Tertiary mirror position (relative to primary vertex)
Image surface:
 dimg
 0.873 m
Image surface diameter (for field of view)
 Cimg
 0.471 m−1
Image surface curvature
 Zimg
 -7.0 m
Image surface position (relative to tertiary exit plane)
Primary Mirror Geometry
The telescope primary mirror geometry is constructed using instances of the Conic Polygonal Mirror Off Axis 3D part 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 (that is, 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 2 and in Figure 3 the complete primary mirror geometry can be seen.
 
Table 2: Primary mirror segment parameters.
Segment
Radial coordinate (r)
Polar Angle ()
Rotation angle ()
1
1.55885 m
0°
30°
2
2.70000 m
30°
0°
3
3.11769 m
0°
30°
4
4.12432 m
- 30°
5
4.12432 m
30° -
6
4.67654 m
0°
30°
Figure 2: 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 3: The primary mirror. The outline of the set of 6 common mirrors is shown in black.
Figure 4: The complete Keck Telescope geometry sequence.
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 and T.S. Mast, Optical Design and Instrumentation of the Keck Observatory, Proc. SPIE 0628, 1986.
2. J.E. Nelson, T.S. Mast, and 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
Click  Done.
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.
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
Click OK.
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:
Name
Expression
Value
Description
R
R_prim
-35 m
Radius of curvature (+convex/-concave)
k
k_prim
-1.0038
Conic constant
Tc
Tc_prim
0.075 m
Center thickness
d0
d0_prim
1.79 m
Mirror full diameter
d_clear
0
0 m
Clear aperture diameter
dx
r1
1.5589 m
Mirror off axis distance
nix
0.0
0
Local optical axis, x-component
niy
0.0
0
Local optical axis, y-component
niz
-1.0
-1
Local optical axis, z-component
nxx
0.0
0
Mirror off axis direction, x component
nxy
1.0
1
Mirror off axis direction, y component
nxz
0.0
0
Mirror off axis direction, z component
n_side
nside
6
Number of polygon sides
phi_rot
phi1
30 °
Polygon rotation angle
mtype
mtype
1
Mirror type (standard [0] or standalone [1])
show_vertex
0
0
Show mirror vertex (off [0] or on [1])
n_extra_r
0
0
Number of extra radial points
n_extra_a
0
0
Number of extra azimuthal points
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
Click OK.
Now, apply each of these selections.
12
In the Settings window for Part Instance, locate the Boundary Selections section.
13
In the table, enter the following settings:
Name
Keep
Physics
Contribute to
Exterior
 
√
None
Mirror surface
 
√
Mirrors
Mirror obstruction
 
√
Obstructions
Mirror rear surface
 
√
Obstructions
Mirror edges
 
√
Obstructions
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:
Name
Expression
Value
Description
dx
r2
2.7 m
Mirror off axis distance
phi_rot
phi2
0
Polygon rotation angle
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:
Name
Expression
Value
Description
dx
r3
3.1177 m
Mirror off axis distance
phi_rot
phi3
30 °
Polygon rotation angle
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:
Name
Expression
Value
Description
dx
r4
4.1243 m
Mirror off axis distance
phi_rot
phi4
-10.893 °
Polygon rotation angle
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:
Name
Expression
Value
Description
dx
r5
4.1243 m
Mirror off axis distance
phi_rot
phi5
10.893 °
Polygon rotation angle
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:
Name
Expression
Value
Description
dx
r6
4.6765 m
Mirror off axis distance
phi_rot
phi6
30 °
Polygon rotation angle
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
Click OK.
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:
Name
Expression
Value
Description
R
R_sec
4.8493 m
Radius of curvature (+convex/-concave)
k
k_sec
-1.6431
Conic constant
Tc
Tc_sec
0.15 m
Center thickness
d0
d0_sec
1.429 m
Mirror full diameter
d1
0
0 m
Mirror surface diameter
d_clear
0
0 m
Clear aperture diameter
d_hole
0
0 m
Center hole diameter
nix
0.0
0
Local optical axis, x-component
niy
0.0
0
Local optical axis, y-component
niz
-1.0
-1
Local optical axis, z-component
n_extra_r
0
0
Number of extra radial points
n_extra_a
30
30
Number of extra azimuthal points
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:
Name
Keep
Physics
Contribute to
Exterior
 
√
None
Mirror surface
√
√
Mirrors
Mirror obstruction
 
√
Obstructions
Mirror rear surface
 
√
Obstructions
Mirror edges
 
√
Obstructions
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
Click OK.
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:
Name
Expression
Value
Description
Tc
75.0[mm]
0.075 m
Mirror thickness
d0
d0_ter
1.04 m
Minor axis diameter
theta
45.0[deg]
45 °
Mirror angle
dx
0
0 mm
Offset from optical axis
nix
0.0
0
Local optical axis, x-component
niy
0.0
0
Local optical axis, y-component
niz
1.0
1
Local optical axis, z-component
nxx
1.0
1
Fold angle direction, x component
nxy
0.0
0
Fold angle direction, y component
nxz
0.0
0
Fold angle direction, z component
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:
Name
Keep
Physics
Contribute to
Exterior
 
√
None
Mirror surface
√
√
Mirrors
Mirror edges
 
√
Obstructions
Mirror rear
 
√
Obstructions
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 4.
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
Locate the Additional Variables section. Select the Count reflections check box. A count of the number of reflections is used as a filter for rendering rays in the ray diagram.
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
-dx1
x
-dy1
y
dz
z
5
Specify the rc vector as
0
x
0
y
1
z
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
vx1
x
vy1
y
-vz
z
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
-dx2
x
-dy2
y
4
Locate the Ray Direction Vector section. Specify the L0 vector as
vx2
x
vy2
y
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
-dx3
x
-dy3
y
4
Locate the Ray Direction Vector section. Specify the L0 vector as
vx3
x
vy3
y
Ray Termination 1
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, from geometry. This will remove those rays that are not reflected by the segmented mirror.
Mesh 1
Edit the default mesh to use finer boundary elements on the curved image surface.
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Sequence Type section.
3
From the list, choose User-controlled mesh.
Size 1
1
In the Mesh toolbar, click  Sizing and choose Size.
2
Drag and drop below Size.
3
In the Settings window for Size, locate the Geometric Entity Selection section.
4
From the Geometric entity level list, choose Boundary.
5
Select Boundary 1 only.
6
Locate the Element Size section. From the Predefined list, choose Extra fine.
7
Click  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
From the Color table transformation list, choose Reverse.
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.