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Design and performance estimate of a focal reducer for the 2.3 m Thai National Telescope

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Abstract

We have designed a new kind of focal reducer for the 2.3 m Thai National Telescope (TNT) to image the TNT specified FOV Δθ = 14.6’ with an angular resolution α ≈1.2 arcsec. This, at a minimum cost by using common glasses, spherical surfaces and by requiring comfortable mechanical tolerance. This focal reducer comprises 1 lens placed at the level of the fork entrance and 1 lens placed in front of the detector. In this paper, we present the focal reducer paraxial model, we describe the optical design and we present the performance.

© 2016 Optical Society of America

1. Introduction

The Thai National Telescope (TNT) is a Ritchey-Chretien Telescope with a primary mirror diameter ΦM1 = 2.3 m and a focal ratio f/10. The TNT is the main instrument of the Thai National Observatory (TNO) which is located near the summit of the Doi Inthanon, situated in the Chiang Mai Province of Thailand at altitude 2,457 meters. The median seeing on this site is αS,Median ≈0.9” and is remarkably stable on most nights, rarely exceeding αS,Max = 2” [1]. Three instruments are currently in operation at the TNT: the ULTRASPEC camera [1], the Medium Resolution Echelle Spectrograph (MRES) and the 4K camera. The ULTRASPEC camera is a high-speed photometer based on an Electron Multiplying CCD with 1k x 1k x 13µm pixels. This camera is used to measure fast varying phenomena such as flares, outbursts and transits. The MRES is a single object fiber-fed Echelle spectrograph providing spectrums with a resolution R ≈15 000 over the spectral band [390-880 nm]. The 4K camera comprises a cryogenically cooled thinned CCD with 4k x 4k x 15µm pixels. This camera is the facility imager for all science goals not requiring high time resolution. The maximum Field Of View (FOV) covered by the TNT in 1 exposure is provided by this 4K camera and is equal to 8.8’ x 8.8’ square while the specified FOV of the TNT is a circle of angular diameter Δθ = 14.6’.

The aims of the focal reducer are: to image the TNT specified FOV on the 4K camera, to correct the telescope optical aberrations and to provide images quality close to the seeing limit. In these conditions, the field coverage provided by the full system would be 3 times larger than the current FOV accessible with the ULTRASPEC camera (7.7' x 7.7' square). That would represent an interesting alternative for the study of extended astronomical objects. The design of the focal reducer has been driven by 3 major constraints. The first constraint is that the installation of the focal reducer on the TNT must not impact the operations of the other instruments. The second constraint is that the overall dimensions must cope with the tiny volumes available for the focal reducer installation. The third constraint is the cost of the focal reducer which must be kept as low as possible. For this reason, the focal reducer must comprise only common glasses, only spherical surfaces and the mechanical tolerances must be achievable by using common manufacturing methods and facilities.

There are 2 major different kind of focal reducer designs [2]. The first kind is the Cassegrain camera, or focal reducer, of Meinel [3] and Courtes [4,5] that comprises a field lens, placed near the Cassegrain focal plane, a collimator, and a camera. This kind of instrument provides the best correction of the image quality and provides very high reduction of the telescope focal. This kind of reducer has been recently installed and commissioned on several instruments [1,6,7]. The problem is that this kind of instrument is complex, expensive, requires a large volume and induces an important displacement of the camera that was not compatible with the accommodation constraints.

The second kind of design consists of placing a group of lenses in front of the camera. This kind of instrument presents the advantage to be very compact and to keep the position of the camera unchanged. This design is widely developed and used for the amateur telescopes. For large telescopes, the correction of the aberration and in particular the lateral chromatism is difficult to perform due to the fact that the lenses are placed close to the image plane and far from the pupil plane. The most recent successful development of this kind of design is the development of the focal reducer the 2.1 m Otto Struve telescope for the CQUEAN (Camera for QUasars in EArly uNiverse) project [8].

In our paper we propose an innovative and low-cost solution to image the TNT specified FOV on the 4K camera. In the section 2 we present the TNT optical design. In the section 3 we discuss the optical specifications used to design the focal reducer. In the section 4 we present the paraxial modelling of the focal reducer. In the section 5 we detail the accommodation constraints. In the section 6 we describe the focal reducer optical design and the theoretical performance. In the section 7 we present the performance budget of the angular resolution performance.

2. The Thai National Telescope

The TNT optical design [9] is represented on the Fig. 1 and comprises 1 hyperbolic primary mirror M1, 1 hyperbolic secondary mirror M2 and 2 plane folding mirrors M3 and M4. The mirror M2 is mounted on a translatable mount with a displacement range equal to 10 mm along the optical axis for the optimization of the focus during the observations. The telescope specified Field Of View (FOV) is ΔθSpec = 14.6 arcminutes and the plate scale is equal to 8.7Arcsec/mm. The TNT is placed on an alta-azimuthal mount with a pointing accuracy better than 3 arcsec RMS at elevation θE = 70° and a tracking accuracy better than 0.5 arcsec RMS over 10 min. The optomechanical design comprises 1 baffle that surrounds the mirror M2, 1 baffle placed inside the mount fork and 1 instrument cube. The baffle placed inside the fork comprises 21 diaphragms which diameters and positions have been adjusted to reject the stray light at the focal plane level [9, 10]. The instrument cube provides mounting locations for up to 4 permanent instruments. It includes a rotating instrument selection mirror (M4) that is computer controlled to select one of the four instrument ports.

 figure: Fig. 1

Fig. 1 TNT ZEMAX optical model.

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The Fig. 2 represents the optical elements located at the instrument cube level. The flange is located at 250 mm from the M4 center. The filter is made of Fused Silica of thickness eFilter = 5 mm and is located inside a filter wheel of thickness eFW = 62 mm. The 4K camera comprises 1 entrance window and 1 cryogenic cooled CCD detector. The entrance window is made of Fused Silica and the thickness of this window is equal to 6.5 mm. The CCD detector is broadband anti-reflective coated and comprises 4096x4096x15.0 micron pixels thus yielding a sensor width l ≈61mm. In this study we assume that the 4K camera will be used in the 2x2 binning mode, the size of each element of resolution is thus equal to 30 μm.

 figure: Fig. 2

Fig. 2 Optical elements and current position of the filter wheel and of the 4K camera at the instrument cube level.

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3. Focal reducer specifications

The TNT focal reducer specifications are represented in the Table 1. The performance shall be guaranteed over the full visible domain [400 nm, 800 nm] and over each of the spectral band of the Johnson-Cousins-Bessell filters B, V, R and I [11]. It is important to mention that our instrument is dedicated to visible and near-infrared applications. The performances are thus not guaranteed in the Johnson-Cousins-Bessell U band filter.

Tables Icon

Table 1. TNT and focal reducer optical performance specifications.

The diameter of the telescope is specified to ΦM1 = 2.3 m that is the current TNT clear aperture [9]. The focal length is specified to be equal to fTNT = 14470 mm to image the full TNT specified FOV on the 4K camera detector. This detector comprises 2048x2048 pixels of 30 μm thus yielding a sensor width l = 61 mm. The specified FOV of the TNT equipped with the focal reducer is circular of diameter ΔθSPEC = 14.6’. The plate scale is equal to 0.42”/pixel and the stellar profile due to the seeing only covers 2 pixels. We admit an enlargement of the stellar profile due to the focal reducer optical aberrations equal to 1 pixel and we specified the angular resolution to be better that 1.3” in median seeing conditions. In this condition, the FWHM of a stellar profile covers about 3 pixels under the typical seeing condition.

We consider that the angular resolution α of the TNT equipped with the focal reducer observing through the atmosphere is: α = (αS 2 + αOptics2)1/2 where αS ≈0.9” is the median seeing at TNO and αOptics is the angular resolution due to the optical aberrations. The angular resolution of the full system being specified to be better that 1.3”, we deduce that αOptics must be lower than 1”. The maximum chief ray angle at the filter level is specified to be lower than 5°. This, in order to avoid significant variations of the central wavelength of narrow band filter over the FOV. We specified the maximum distortion to be lower than 1% to keep this distortion at a reasonable level. Finally, we specified the optical design of the focal reducer by using spherical surfaces and common glasses to minimize the cost.

4. Paraxial modelling

The focal reducer design comprises 1 lens located at the fork entrance and 1 lens located in front of the camera. The aim of the paraxial modelling is to calculate the focal of these lenses to respect the constraints on the image position and magnification. On the one hand, the image plane of the focal reducer must be located at the current image TNT image plane. On the other hand, the magnification of the focal reducer must be adjusted to image the specified FOV on the 4K detector.

The Fig. 3 represents the exit pupil and the focal plane of the TNT in the case “without focal reducer”. The exit pupil diameter is ΦExP = 0.57 m and the distance between this pupil and the image plane is dExP = 5.8 m. The object AB (not represented in the Fig. 3) is located at infinity and the angular extension of AB is ΔθSPEC = 14.6’. The size of the image A1B1 is thus y1 ≈ΔθSPEC.fTNT where fTNT = 24 m is the TNT focal without the focal reducer. In this condition, the size of the image is y1 ≈104 mm.

 figure: Fig. 3

Fig. 3 Paraxial model of the TNT without the focal reducer.

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The Fig. 4 represents the TNT exit pupil, the focal reducer and the image plane. The lens L1 is positioned at the TNT fork entrance which is located at the distance d1 = 4.3 m from the exit pupil. The lens L2 is positioned at the cube flange level which is located at the distance d2 = 1.4 m from the fork entrance (i.e. from L1). The 4K camera focal plane is located at the distance d3 = 0.13 m from the cube flange (i.e. from L2).

 figure: Fig. 4

Fig. 4 TNT and focal reducer paraxial model.

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The relation between d1, d2 and d3 to ensure that the position of the 4K camera will be identical with and without the focal reducer is d1 + d2 + d3 = dExP. By applying the conjugate relations between A1B1 and A2B2, we deduce the Eq. (1):

f2'=A.f1'+B
Where:
A=d32/(d2+d3)2
And:

B=d2.d3/(d2+d3)

The size of A2B2 is y2 = γ. y1 where γ is the focal reducer magnification. The aim of the focal reducer is to image the object A2B2 on the 4K camera sensor width l = 61 mm, we thus deduce that γ = 0.6. By applying the conjugate relations between A1B1 and A2B2, we deduce the Eq. (4) between f1’ and f2’ to respect the constraint on the image dimension:

f2'=1/(C/f1'+D)
Where:
C=γ.(d2+d3)/d3
And:

D=(1γ)/d3

The analytical expressions of f1’ is thus obtained by equalizing the expressions (1) and (4) thus yielding the Eq. (7). The corresponding value for f2’ is obtained by applying the Eq. (1) or the Eq. (4).

(A.D).f1'2+(A.C+B.D1).f1'+B.C=0

We found 2 couple of solutions: solution 1 (f1’ = −26 m, f2’ = 0.3 m) and solution 2 (f1’ = −1.53 m, f2’ = 0.13 m). We selected the solution 1 that provides the highest focal length values in order to maximize the image quality and the robustness to alignment and integration errors.

5. Accommodation constraints

We have identified 2 accommodation constraints at the fork level that drive the L1 design. The first constraint concerns the maximal thickness of L1 which must be adjusted to avoid the vignetting of the beams incident on the M1 (Fig. 5). The fork entrance is located at the distance dFork = 210 mm from the entrance pupil upper edge. We thus decided to set the L1 maximal thickness to dL1,Max = 200 mm and to keep a 10 mm margin for the accommodation of the L1 barrels. The second constraint concerns the clear aperture of the lenses L1. This clear aperture must be adjusted to avoid the vignetting of the beam incident on the baffle by the lens edges. The diameter of the vane located at the baffle entrance is ΦBaffle = 200 mm. By applying a typical margin of 10%, we deduce that the L1 minimum diameter is ΦL1,min = 220 mm.

 figure: Fig. 5

Fig. 5 Mechanical constraints at TNT fork entrance level for the accommodation of focal reducer lens L1.

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We have identified 4 accommodation constraints at the instrument cube level that drive the L2 design. The first constraint is that the distance dM4-L2 between L2 front face and the mirror M4 (Fig. 6) must be adjusted to avoid any contact with the mount during the rotation of the mirror for the instrument selection. We measured the available distance inside the cube and we assessed that dM4-L2 must be must be higher than 200 mm to respect this constraint. The distance between the M4 center and the flange being dCube = 250 mm, we deduce that the maximum available distance inside the cube for L2 assembly is thus dL2-Flange = dCube - dM4-L2 = 50 mm.

 figure: Fig. 6

Fig. 6 Accommodation constraints at the instrument cube levels for the accommodation of focal reducer lens L2.

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The second constraint concerns the maximum distance dWheel between the filter wheel and the instrument cube flange. This distance must be lower than 50 mm to ensure the feasibility of the fixation of the 4K camera and the filter wheel on the cube. The L2 thickness being dL2 = dL2 Flange + dWheel, we deduce that dL2 must be lower than 100 mm.

The third constraint is that the L2 front face minimum diameter ΦL2 must be adjusted to ensure that the lens edges will not vignette the incident beam. We assessed that the incident beam diameter at the L2 entrance level is equal to 132 mm. By applying a typical margin of 10%, we deduce that the L2 front face minimum diameter is ΦL2,min = 145 mm. The fourth constraint concerns the L2 maximum diameter which must be adjusted to ensure the mechanical feasibility and rigidity of the L2 barrel. We consider that such a barrel would require a minimum material thickness equal to 20 mm. The aperture diameter of the flange being ΦCube = 242 mm, we deduce that the maximal diameter of L2 is ΦL2, Max = 202 mm. The Table 2 presents a summary of the mechanical constraints for the lenses L1 and L2.

Tables Icon

Table 2. Focal reducer L1 and L2 lenses dimension specifications

6. Focal reducer design and performance

6.1 Design

The design of the focal reducer has been performed by using the Zemax software and comprised 3 steps described hereafter. The first step consisted of optimizing the lens L1 only with paraxial models of the TNT and of the lens L2. The second step consisted of optimizing the lens L2 only with paraxial models of the TNT and of the lens L1. The third step consisted of optimizing the full system including: the as-built model of the TNT, the L1 design (step 1 output) and the L2 design (step 2 output). The focal reducer design is represented in the Fig. 7.

 figure: Fig. 7

Fig. 7 Focal reducer optical design.

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The lens L1 is an achromatic doublet that comprises 2 lenses L11 and L22 made of BK7 and F2 glasses respectively. This lens would be placed on a sliding rail and would be removed from the optical path during the operation of the other instruments mounted on the instrument cube. The surfaces are spherical and the geometrical parameters are summarized in the Table 3. The lens L1 includes 1 stop of diameter of Φ = 200 mm placed in front of the lens L11. This stop blocks the light scattered by the opto-mechanical structure to minimize the stray light at the detector level as described in previous papers dedicated to the improvement of the TNT stray light performance [9,10]. After optimization, the L1 image quality was diffraction limited and the lens position and diameters complied with the mechanical constraints.

Tables Icon

Table 3. Focal reducer lens properties (units are mm).

The lens L2 (Fig. 8) is a triplet that comprises 1 converging lens L21 made of S-PMH52, 1diverging lens L22 made of SF1 and 1 converging lens made of N-PSK53-A. The surfaces are spherical and the geometrical parameters are summarized in the Table 3. The lens L2 includes 1 field stop of diameter ΦFS = 122 mm that blocks the off-axis rays from objects located outside the specified FOV to minimize the stray light at the detector level.

 figure: Fig. 8

Fig. 8 Focal reducer L2 lens close view.

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6.2 Spot diagrams and ray fans

The Fig. 9, the Fig. 10 and the Fig. 11 represent respectively the spot diagrams, the chromatic focal shift and the ray fans of the TNT equipped with the focal reducer after the final optimization of the system. These performance are presented over the spectral domain [400 nm, 800 nm] and for 3 FOV samples: FOV 1 (0’, 0’) located at the FOV center, FOV 2 (0’, 4.8’) located at an off-axis distance equal to 2/3 of the specified FOV and FOV 3 (0’, 7.3′) located at the edge of the specified FOV.

 figure: Fig. 9

Fig. 9 Spot diagrams of the TNT equipped with the focal reducer on the spectral band [400 nm, 800 nm] at the FOV 1 (0, 0’), FOV 2 (0’, 4.8’) and FOV 3 (0’, 7.3′). The central box represents 1 pixel of size 30 μm x 30 μm.

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 figure: Fig. 10

Fig. 10 Chromatic focal shift of the TNT equipped with the Focal Reducer.

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 figure: Fig. 11

Fig. 11 Ray fans of the TNT equipped with the focal reducer on the spectral band [400 nm, 800 nm] at the FOV 1 (0’, 0’), FOV 2 (0’, 4.8’) and FOV 3 (0’, 7.3′).

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We notice on the Fig. 9 that the spot diameter is always lower than 64 μm RMS (2 pixels approximatively). We also notice on the Fig. 10 that the system is fully corrected of the axial chromatism. Indeed, the chromatic focal shift is ΔL = 30 μm that induces a negligible variation of the spot size δΦ ≈5 μm. The main aberration is the lateral chromatism. Indeed, in the ray fans (Fig. 11), we notice that the maximum distance between the chief ray impacts at λ = 500 nm and λ = 800 nm is equal to 65 μm (2 pixels approximatively). However, the RMS spot diameter equal to 64 μm and the calculation of the angular resolution over the FOV demonstrate that the system is compliant to the specifications on the image quality as described in the next section.

6.3 Angular resolution theoretical performance

We define the angular resolution as α = ΦSpot/fTNT where ΦSpot is the diameter that corresponds to an Encircled Enery (EE) equal to 76%. This definition is consistent with the definition of the seeing. Indeed, if we assume that the star profile after propagation through the atmosphere is a Gaussian distribution, the energy integrated over a circle of diameter equal to the FWHM is equal to 76% of the total energy [12]. The Fig. 12 represents the variation of the angular resolution αTh due to the optical aberrations of the theoretical system by assuming perfect optical surfaces and positioning. This, over a 14.6’ x 14.6’ FOV and over the spectral domain [400 nm, 800 nm]. The Table 4 represents the angular resolution mean value <αTh>, the variance σα and the maximum value of αTh, Max over the specified FOV.

 figure: Fig. 12

Fig. 12 Angular resolution variations over the FOV (left) and histogram of the angular resolution values over the specified FOV (right).

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Tables Icon

Table 4. Angular resolution mean value <αTh>, standard deviation σα and maximum value αTh, Max over the specified FOV for the specified spectral bands.

We notice that the mean value of angular resolution is always lower than 0.7” over the full spectral domain [400 nm, 800 nm] and over the spectral band of each Johnson-Cousins filters B, V, R and I. Only the maximal value αTh, Max is equal to 1”. However, this maximum value is reached at the extreme edge of the specified FOV only. Furthermore we notice that the angular resolution is particularly stable over the full FOV since the maximum standard deviation σα is equal to 0.1”. For this reason, we consider that the angular resolution of the system is equal to <αTh> = 0.75” and we use this value to establish the performance budget presented in the next section.

6.4 Distortion and chief ray incidence angle

The maximum distortion of the system is equal to 0.1% that is fully compliant with the specification. The maximum angle of incidence on the filter is θi, Max = 8° that is higher than the specification equal to 5°. The consequence will be a variation of the interference filter spectral band response over the FOV. For a narrow band filter of central wavelength λ0 for on-axis light and of equivalent index of refraction n*, the shift of the central wavelength at the angle of incidence θi is given by the Eq. (9) [13,14]:

Δλ=λ0[1cos(arcsin(sinθi/n*))]

For example, the central wavelength shift of a Hα filter of λ0 = 658.6 nm and of n*≈1.9 at θi, Max = 8° would be Δλ ≈1.8 nm. Some solutions already exist to cope with this in-field variation of the filters spectral response: careful specification of the narrow band filters [14,15] and proper characterization of the in-field variations of the photometric filter responses to apply the relevant photometric corrections [16,17]. For this reason, we consider that this non-compliance is acceptable.

7. Angular resolution performance budget

7.1 Fabrication errors assumptions and sensitivity analysis results

The assumptions for the precision of the lens fabrications are based on the manufacturing precisions of the company Optimax [18] and are summarized in the Table 5. That comprises the following contributors: index of refraction and Abbe number precisions, surface irregularities, radius of curvature precision and the tilts and decenters of the lens surfaces.

Tables Icon

Table 5. Fabrication parameters.

In a first step we performed a sensitivity analysis to analyze the impact of the parameter amplitudes presented in the Table 5. This sensitivity analysis was performed at the edge of the specified FOV that was identified as the FOV region the most sensitive to the fabrication errors. In a second step we have identified the critical parameters that induce a loss of EE higher than 1% at the radius r = 35 μm from the spot centroid corresponding to an angular radius equal to 0.5”. This, after the optimization of M2 position to compensate the aberration of pure focus. These critical parameters are: the tilt of each lens that induce a maximum EE loss equal to 2% and the precision on the Abbe number that induces a EE loss equal to 1%. The other parameters induce a variation of EE lower than 1% and are thus not critical.

7.2 Mounting and alignment error assumptions and sensitivity analysis results

The contributors to the mounting errors are the decenters and the tilt errors of each single lens L11, L12, L21, L22 and L23 with respect to the theoretical positions. We have assumed that the maximum position and tilt errors of each single lens were equal to 100 μm and 0.1° respectively. The alignment error comprises the decenter of each lens L1 and L2 with respect to the theoretical position.

The contributors to the alignment errors are the maximum position and tilt errors of L1 and L2 assemblies with respect to the theoretical positions. L1 will be mounted on a rail and position in front of the fork during the observations. For this reason, we have assumed that the L1 alignment errors in position will be equal to 1 mm along the transverse direction X and Y and equal to equal to 5 mm along the optical axis Z. We also assumed that L1 will be mounted on a stable precision tip-tilt mount and that the maximum tilting error around X and Y will be equal to 0.1°. The lens L2 will be mounted on the flange of the instrument cube. We assume that the telescope is perfectly aligned and that the Nasmyth cube flange center is located on the optical axis. The alignment precision of the lens L2 will thus be driven by the manufacturing precision of the L2 mount. We thus assume that the L2 alignment errors in position will be equal to 0.1 mm along each direction X, Y and Z and that the maximum tilting error around X and Y will be equal to 0.1°.

We have performed the same kind of sensitivity analysis as presented in the previous section and we have identified the following critical parameters: the tilt of the single lens L21, L22, L23 and the global tilt of the L2. The maximum EE variation due to these misalignment was equal to 2%. It is important to precise that the lens L1 is robust with respect to the mounting and alignment errors since the EE variations induced by each parameter of the sensitivity analysis were lower than 1%. That confirms the possibility to mount the lens L1 on a sliding rail to place the lens in the optical path for the observations with the focal reducer and to remove the lens for the operation of the other instruments mounted on the instrument cube.

7.3 Performance budget

For each contributor, we have performed a tolerancing analysis to assess the angular resolution loss due to the manufacturing errors. This tolerancing analysis was obtained over a statistic of 800 optical systems for the fabrication errors, 250 systems for the mounting errors and 100 systems for the alignment errors sorted over a normal law. For each system, we optimized the M2 axial position (compensator) to be representative of the conditions of observation with the TNT. The Table 6 represents the losses of angular resolution δαFabrication, δαMounting and δαAlignment due to the fabrication, the mounting and the alignment respectively for the [400 nm, 800 nm] spectral domain. This, in the “typical case” at 1σ (68% of the systems), in the “realistic case” at 2σ (95% of the systems) and in the “worst case” at 3σ (99.7% of the systems). We have also represented the total loss of angular degradation δα that is the quadratic summation of δαFabrication, δαMounting and δαAlignment. It is important to mention that the maximum displacement of the compensator was equal to 0.1 mm that is fully compatible with the M2 mirror displacement range equal to +/− 5 mm.

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Table 6. Results of the tolerancing analysis for the Fabrication, Mounting and alignment errors.

We notice that the major contribution to the angular resolution loss is the fabrication. Indeed, in the realistic case, the δαFabrication = 0.06” while δαMounting and δαAlignment are both equal to 0.02”. We thus deduce that the final performance will be dominated by the impact of the fabrication errors on the theoretical performance. We also notice that the angular resolution loss after fabrication, mounting and alignment is negligible in the typical case and 10 times lower than the theoretical performance in the realistic case. In the worst case, the loss reaches 0.11” but this case would mean that all the errors are maximum simultaneously that is very unlikely to occur.

The Table 7 represents the performance budget of the focal reducer angular performance. The angular resolution αFR of the system is the quadratic summation of the angular resolution αS due to the seeing, the theoretical angular resolution αTh of the system by assuming perfect optical surfaces and perfect positions and orientations and the angular resolution loss δα due to the fabrication, the mounting and the alignment. We notice that αR ≈1.2” that is compliant with the specifications. In this condition, the stellar profile is 30% larger that the limit imposed by the seeing. We thus consider that this performance is acceptable and that the focal reducer will provide images of astronomical object of extension up to 14.6’ with an angular resolution close to the seeing limit in median conditions.

Tables Icon

Table 7. Angular resolution performance budget on the [400 nm, 800 nm] spectral domain.

8. Conclusions

We have presented the design and the performance of a new kind of focal reducer for the 2.3 m Thai National Telescope. This instrument comprises only spherical surfaces and common glasses and the tolerance for the fabrication the mounting and the alignment are in line with the common methods and facilities. The proposed design is fully compliant with the stringent accommodation constraints and the performance are in line with the specifications. In particular, we have demonstrated that the angular resolution is close to the seeing limit and is very stable over the full specified FOV. The only limitation is the variation of the chief ray angle on the filter that could induce a very slight in-field variation of the spectral response. However, already existing methods proposes adequate solutions to this problem. We thus consider that the proposed design is a good compromise between the cost and the performance. Finally, we would like to emphasize that the design method is universal and can be applied to any kind of 2 meter-class telescope to increase the FOV at a minimum cost.

The future development of the focal reducer will comprise 3 steps. The first step will consist of performing the stray light analyses and specifying the anti-reflective coating performance to ensure that the focal plane will be free of critical ghost images. The second step will consist of defining the mechanical and electronical design of the focal reducer and of the associated support. The third step will consist of procuring the equipment, integrating the full system on the TNT and commissioning the instrument.

Acknowledgments

Assoc Pr Thierry Lépine and Mr Alexis Deboos acknowledge the National Astronomical Research Institute of Thailand (NARIT) for the financial support provided to perform the work on the focal reducer presented in this paper.

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17. M. A. Quijada, C. T. Marx, R. G. Arendt, and S. H. Moseley, “Angle-of-incidence effects in the spectral performance of the infrared array camera of the Spitzer Space Telescope,” Proc. SPIE 5487, 244–252 (2004). [CrossRef]  

18. OPTIMAX website, http://www.optimaxsi.com/innovation/optical-manufacturing-tolerance-chart/ (2015).

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Figures (12)

Fig. 1
Fig. 1 TNT ZEMAX optical model.
Fig. 2
Fig. 2 Optical elements and current position of the filter wheel and of the 4K camera at the instrument cube level.
Fig. 3
Fig. 3 Paraxial model of the TNT without the focal reducer.
Fig. 4
Fig. 4 TNT and focal reducer paraxial model.
Fig. 5
Fig. 5 Mechanical constraints at TNT fork entrance level for the accommodation of focal reducer lens L1.
Fig. 6
Fig. 6 Accommodation constraints at the instrument cube levels for the accommodation of focal reducer lens L2.
Fig. 7
Fig. 7 Focal reducer optical design.
Fig. 8
Fig. 8 Focal reducer L2 lens close view.
Fig. 9
Fig. 9 Spot diagrams of the TNT equipped with the focal reducer on the spectral band [400 nm, 800 nm] at the FOV 1 (0, 0’), FOV 2 (0’, 4.8’) and FOV 3 (0’, 7.3′). The central box represents 1 pixel of size 30 μm x 30 μm.
Fig. 10
Fig. 10 Chromatic focal shift of the TNT equipped with the Focal Reducer.
Fig. 11
Fig. 11 Ray fans of the TNT equipped with the focal reducer on the spectral band [400 nm, 800 nm] at the FOV 1 (0’, 0’), FOV 2 (0’, 4.8’) and FOV 3 (0’, 7.3′).
Fig. 12
Fig. 12 Angular resolution variations over the FOV (left) and histogram of the angular resolution values over the specified FOV (right).

Tables (7)

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Table 1 TNT and focal reducer optical performance specifications.

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Table 2 Focal reducer L1 and L2 lenses dimension specifications

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Table 3 Focal reducer lens properties (units are mm).

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Table 4 Angular resolution mean value <αTh>, standard deviation σα and maximum value αTh, Max over the specified FOV for the specified spectral bands.

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Table 5 Fabrication parameters.

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Table 6 Results of the tolerancing analysis for the Fabrication, Mounting and alignment errors.

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Table 7 Angular resolution performance budget on the [400 nm, 800 nm] spectral domain.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

f 2 ' =A. f 1 ' +B
A= d 3 2 / ( d 2 + d 3 ) 2
B= d 2 . d 3 / ( d 2 + d 3 )
f 2 ' =1/ ( C/ f 1 ' +D )
C=γ. ( d 2 + d 3 ) / d 3
D= ( 1γ ) / d 3
( A.D ). f 1 ' 2 +( A.C+B.D1 ). f 1 ' +B.C=0
Δλ= λ 0 [ 1cos( arcsin( sin θ i / n * ) ) ]
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