Modeling the segmented primary for a 10 meter – class telescope. Vineeth Valsana , S. Srirama , Annu Jacoba , J. P. Lancelota and G. C. Anupamaa a
Indian Institute of Astrophysics, Bangalore, Karnataka, India. ABSTRACT
The primary mirror for a 10 meter class telescope will be made of many individual segments rather than a monolithic mirror, because of the ease with which the segments can be made, transported and replaced. An f1 primary mirror with an RoC of 20 meter is modeled using Zemax. The theoretical evaluation of the basic properties of the individual segments such as dimensions, orientation and location, has been carried out. The dimensions of each segment is different because the primary mirror is curved and aspheric. These parameters are further optimised with respect to the image spot size and also to minimise the narrow, uniform gap between the segments. The results of this optimisation is discussed in this paper. Keywords: Primary mirror, Optical telescope, Segmented telescope, segmented mirror
1. INTRODUCTION The primary mirror of a large telescope is constructed from a number of segmented mirrors. This will make the manufacture, transportation and maintenance much easier than when constructed with a single large mirror. Only the primary mirror has been modeled here. The aberrations due to the primary will be further taken care of by the secondary mirror. Hence in this paper, the basic constraint will be to optimise all the segments of the primary by minimising the focal spot size. Primary mirror segmentation studies has been extensively done1, 2 for Thirty Meter Telescope (TMT) project.3 Each segment in TMT primary has been optimised for various parameters.4 In this paper, the dimensions of the segments is taken equal to that of the segments for TMT. Each segment is hexagonal in shape and measures approximately 1.44 meter between opposite corners and has a thickness of 45mm. The primary mirror is designed with a conic of -1.000928 (hyperbola). All the off-axis segments can be divided into 6 sectors, because of the 6 fold symmetry of the primary mirror, as shown in Figure 1. The dimensions of each segment in a sector will be unique due to the aspheric nature of the primary. Table 1. Parameters of the 10 meter segmented primary mirror.
Parameter
Value
Diameter F# Conic constant No. of segments Shape of segment Diameter of each segment
10 meter 1 -1.000928 61 Hexagon 1.44 meter
Further author information: (Send correspondence to Vineeth Valsan) E-mail:
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Figure 1. The centroid of each segments of the primary mirror. All the off-axis segments can be divided into 6 equal sectors. The shape of each segment in a sector will be unique.
Figure 2. illustration showing the Segment layout in the 10 meter primary mirror. The circle shows the circumference with diameter equal to 10 meter.
2. MODELING THE SEGMENTED PRIMARY A segmented primary mirror is modeled in sequential mode using the multi-configuration capability of Zemax. We have modeled one segment per configuration. Figure 2 shows the layout of the primary mirror with all the
n Figure 3. Shaded model of 10 meter–class segmented primary mirror.
61 segments. Other parameters involved in modeling are given in Table 1. The focal length of the primary is initially fixed at 10 meters. Later, while optimising, this parameter is kept as a variable. The model is also optimised for minimising the focal spot size. The other parameter that is varied is the conic of the primary.
2.1 Spot diagram After optimisation, the focus spot has an RMS radius of 22.873 µm (the airy diameter being 9.81 µm). It has a geometric radius of 49.129 µm. Figure 4 shows the image plane with the spot diagram. Here the centroid of the spot is the reference point. The ray density is 3 per configuration.
Figure 4. Spot Diagram at the focus of the segmented primary, after optimisation.
2.2 PSF and the Encircled energy Figure 5 shows the normalised Huygens PSF (on-axis) of the segmented primary. Figure 6 gives the fraction of energy enclosed with respect to the radius from the centroid of the spot on the imaging surface.
Figure 5. The Huygens Point Spread Function of the segmented primary.
The diffraction limited case is also shown for comparison. It may be noted that 50% of the energy has been encircled within a radius of 7 µm. The cross section of the normalised Huygens PSF is shown in Figure 7.
Figure 6. Encircled Energy of the spot at the image plane.
2.3 RMS Wavefront Error RMS wavefront errors with respect to wavelength (Figure 8) and Focus (Figure 10) is plotted. The wavefront error is 0.25 waves at 550 nm wavelength.
2.4 Configuration matrix spot diagram The spot diagram on the image plane of different configurations has been plotted seperatley and is given in Figure 9. As can be seen the segments which are far off axis diviate from the centroid of focus spot more than that of the inner segments.
Figure 7. Cross section of the Huygens PSF.
Figure 8. RMS wavefront error plotted against Wavelength. The diffraction limit is also shown.
Figure 9. The spot diagram on the image plane of all the segments plotted seperately.
3. SUMMARY The segmented primary mirror of a 10 meter–class telescope has been modeled with 61 segments of dimension approximately 1.44m between opposite edges and thickness 45mm. The shape of the mirror sag is hyperbolic with a conic constant of -1.000928. The focal length of the optimised segmented primary is 10.000 meters. This gives an f# of 1. The inter segment spacing is 5mm. The larger the space between the segments, lower is the light gathering capacity of the primary. The RMS spot radius is 22.873 µm. The induced aberrations of the primary has to corrected with an appropriate secondary mirror.
Figure 10. RMS wavefront error with respect to focus shift. The diffraction limit is also shown.
REFERENCES [1] Mast, T. and Nelson, J., “TMT - internal communication: TMT primary mirror segment shape.” TMT Report No. 58 (2004). [2] Seo, B. J., Nissly, C., Angeli, G., MacMynowski, D., Sigrist, N., Troy, M., and Williams, E., “Investigation of primary mirror segment’s residual errors for the thirty meter telescope,” in [Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series], Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 7427 (aug 2009). [3] “Thirty Meter Telescope (TMT ).” http://www.tmt.org. [4] Baffes, C., Mast, T., Nelson, J., Ponslet, E., Stephens, V., Stepp, L., and Williams, E. C., “Primary mirror segmentation studies for the thirty meter telescope,” in [Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series], Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 7018 (jul 2008).
