Hubble Space Telescope

The Hubble Space Telescope (HST) is an example of a standard Cassegrain telescope. This tutorial demonstrates how to use the Conic Mirror On Axis 3D part from the Part Libraries to construct the HST Ritchey-Chrétien geometry, and how to include multiple ray release features so that rays at several field angles can be traced simultaneously. An overview of the HST is shown in Figure 1.

Figure 1: Overview of the Hubble Space Telescope.

Model Definition

Details of the Hubble Space Telescope can be found in Ref. 1 and Ref. 2. This is the nominal pre-launch design. In this tutorial the as-built details (see, for example, Ref. 3 and Ref. 4) are not considered, but additional information from these references was used to create the model. A summary of the HST parameters used in this tutorial is given in Table 1.

In this simulation the telescope geometry is constructed using two instances of the Conic Mirror On Axis 3D from the Part Libraries. The image surface is defined using a primitive with the appropriate Petzval curvature. A secondary obstruction has been created using an instance of the Circular Planar Annulus 3D which can also be found in the Part Libraries. The resulting Hubble Space Telescope geometry sequence is shown in Figure 2.

Table 1: HUBBLE SPACE 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	10	Number of hexapolar rings
Pnom	2400.0 mm	Entrance pupil diameter
Primary mirror:
Rprim	-11040.0 mm	Primary mirror radius of curvature
kprim	-1.0022985	Primary mirror conic constant
d0,prim	2450.0 mm	Primary mirror full diameter (nominal)
dh,prim	600.0 mm	Primary mirror central hole diameter
Tc,prim	125.0 mm	Primary mirror center thickness (nominal)
Secondary mirror:
Rsec	1358.000 mm	Secondary mirror radius of curvature
ksec	-1.49600	Secondary mirror conic constant
dsec	395.0 mm	Secondary mirror diameter
Tc,sec	75.0 mm	Secondary mirror center thickness (nominal)
Positions:
Zprim	0 mm	Primary mirror position
Zsec	-4906.071 mm	Secondary mirror position
Zbfl	1500.0 mm	Image surface back focal length (relative to primary vertex)
Zimage	Zsec − Zbfl	Image surface position (relative to secondary surface)
Misc:
εobs	0.33	Obstruction fraction
Cp		Image Petzval curvature

Figure 2: The Hubble Space Telescope geometry sequence.

Figure 3: The Hubble Space Telescope mesh.

Results and Discussion

A ray trace has been performed at a single wavelength (550 nm) at three field angles (0, 5 and 10 arcminutes). Figure 4 shows the resulting ray trajectories; the represents the ray positions on the image surface.

In Figure 5 the intersection of the rays with the image surface is shown. This spot diagram shows each of the three field angles, where the is the initial radial location at the entrance pupil.

Figure 4: Ray diagram of the HST colored by radial distance from the centroid.

Figure 5: Spot diagram of the HST colored by radial distance from the center of the entrance pupil. The absolute coordinate of each spot is shown. The ring in the lower-left corner is the nominal Airy ring.

References

1. C. Burrows, Hubble Space Telescope: Optical telescope assembly handbook. Space Telescope Science Inst., Baltimore, MD, 1990.

2. D. Schroeder, Astronomical Optics. Second Edition. San Diego, CA, USA: Academic Press, 2000.

3. D. Moore and others, Final Report Hubble Independent Optical Review Panel. Goddard Space Flight Center, Greenbelt, MD, 1991.

4. L. Allen and others, The Hubble Space Telescope Optical Systems Failure Report. NASA, 1990.

Ray_Optics_Module/Lenses_Cameras_and_Telescopes/hubble_space_telescope

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file hubble_space_telescope_parameters.txt.

Component 1 (comp1)

In the window, click .

In the window for , locate the section.

Find the subsection. From the list, choose . 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 cubic geometry shape order usually introduces less discretization error compared to the default, which uses linear and quadratic polynomials.

Part Libraries

In the toolbar, click

and choose .

In the window, under click .

In the window, select in the tree.

Click

In the dialog box, select in the list.

Click .

Geometry 1

Primary Mirror

In the window, under click .

In the window for , type Primary Mirror in the text field.

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


Name	Expression	Value	Description
R	R_prim	-11.04 m	Radius of curvature (+convex/-concave)
k	k_prim	-1.0023	Conic constant
Tc	Tc_prim	0.125 m	Center thickness
d0	d0_prim	2.45 m	Mirror full diameter
d1	0	0 m	Mirror surface diameter
d_clear	0	0 m	Clear aperture diameter
d_hole	dh_prim	0.6 m	Center hole diameter
nix	nix	0	Local optical axis, x-component
niy	niy	0	Local optical axis, y-component
niz	niz	-1	Local optical axis, z-component
n_extra_a	np_extra	10	Number of extra azimuthal points

Locate the section. Find the subsection. In the text field, type Z_prim.

Click

Click to expand the section. In the table, select the check box for .

Click to select row number 3 in the table.

Click .

In the dialog box, type Obstructions in the text field.

Click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Keep	Physics	Contribute to
Mirror rear surface		√	Obstructions
Mirror edges		√	Obstructions

Secondary Mirror

In the toolbar, click

and choose .

In the window for , type Secondary Mirror in the text field.

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


Name	Expression	Value	Description
R	R_sec	1.358 m	Radius of curvature (+convex/-concave)
k	k_sec	-1.496	Conic constant
Tc	Tc_sec	0.075 m	Center thickness
d0	d_sec	0.395 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

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

From the list, choose .

Find the subsection. In the text field, type Z_sec.

Click

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


Name	Keep	Physics	Contribute to
Mirror surface	√	√	None
Mirror rear surface		√	Obstructions
Mirror edges		√	Obstructions

Image Surface

A parametric surface can be used to define the image surface.

In the toolbar, click

and choose .

In the window for , type Image Surface in the text field.

Locate the section. Find the subsection. In the text field, type -hw_image.

In the text field, type hw_image.

Find the subsection. In the text field, type -hw_image.

In the text field, type hw_image.

Locate the section. In the text field, type s1.

In the text field, type s2.

In the text field, type Cp*(s1^2 + s2^2)/(1 + sqrt(1 - Cp^2*(s1^2 + s2^2)))*1[m]. This is the equation of a sphere having a curvature Cp. This is the Petzval curvature defined in the Parameters node.

Locate the section. In the text field, type Z_image.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. Select the check box.

Part Libraries

The secondary mirror mount creates an obstruction.

In the toolbar, click

and choose .

In the window, click .

In the window, select in the tree.

Click

Geometry 1

Secondary Obstruction

In the window, under click .

In the window for , type Secondary Obstruction in the text field.

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


Name	Expression	Value	Description
d0	d0_obs	0.792 m	Diameter, outer
d1	0	0 m	Diameter, inner

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

From the list, choose .

Find the subsection. In the text field, type Z_obs.

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


Name	Keep	Physics	Contribute to
All		√	Obstructions

Click

Click the

button in the toolbar.

Click the

button in the toolbar.

Click the

button in the toolbar. Compare the resulting geometry to Figure 2.

Geometrical Optics (gop)

In the window, under click .

In the window for , locate the section.

Click

Locate the section. In the text field, type 0.

Select the 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.

Primary

In the toolbar, click