título esopo error-budget notes - instituto de astronomía · esopo presupuesto de errores...

INSTITUTO DE ASTRONOMÍA

UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO

Espectrógrafo óptico de mediana y baja dispersión para el

Observatorio de San Pedro Mártir

Fecha: 15/01/07 Código: ESOPO-OP-A-PE1 No. de páginas : 24 Versión: 1

Título

ESOPO Error-Budget Notes DOCUMENTO DE TRABAJO

ESOPO

PRESUPUESTO DE ERRORES

CÓDIGO: ESOPO-OP-A-PE1 VERSIÓN: 1

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Control del documento

Preparado por

J. Jesús González

Diseño y Responsable Óptico de ESOPO

Científico del Proyecto

y

Francisco Cobos

Diseñador óptico

Francisco Murillo

Responsable del Error Budget

Revisado por

Carlos Tejada

Diseñador óptico

Responsable de Ingeniería de Sistemas de ESOPO (IAUNA-CU)

Aprobado por

Alejandro Farah

Gestor del Proyecto

Autorizado por

Rafael Costero

Investigador Principal

Juan Echevarria

Responsable del Proyecto

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Registro de cambios (A)

Número Fecha Sección Página Descripción del cambio

1 J. Jesús González escribe documento

2 F. Cobos lo introduce en formato actual, revisa y elabora el documento de trabajo en versión 0

3

4

5

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Lista de abreviaciones

ESOPO Espectrógrafo óptico de mediana y baja dispersión para el Observatorio de San Pedro Mártir

RAN Requerimiento de Alto Nivel

OAN Observatorio Astronómico Nacional

IA-UNAM Instituto de Astronomía de la Universidad Nacional Autónoma de México

EB Error Budget: Presupuesto de Errores

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DOCUMENTACIÓN APLICABLE

Requerimientos de Alto Nivel: (ESOPO-CI-A-REAN1)

Sistema de Coordenadas de ESOPO:

ESOPO AIV Plan:

Diseño Óptico de ESOPO y Especificaciones Ópticas: (ESOPO-OP-A-DO1)

Especificaciones Mecánicas: (ESOPO-ME-A-EM1)

Sistema de rejilla y máscaras: (ESOPO-ME-A-RM1)

Interfaces: (ESOPO-ME-A-IM1)

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ÍNDICE

1. ESOPO ERROR-BUDGET INTRODUCTION ........................................................... 7

2. ESOPO RESOLUTION REQUIREMENTS ................................................................ 9

2.1 DESIGN CONSIDERATIONS ............................................................................................... 10

3. ESOPO ERROR-BUDGET DEFINITIONS AND THE EXCEL SPREADSHEET.10

3.1 OPERATIONAL DEFINITIONS............................................................................................. 10

3.1.1 Resolution-measure Definition.......................................................................... 11

3.1.2 Resolution variation along slit and wavelength .............................................. 12

3.1.3 Changes in relative wavelength/spatial calibration ........................................ 12

3.2 SLIT EFFECTS ................................................................................................................... 12

3.3 GENERAL DESCRIPTION................................................................................................... 12

3.4 MECHANICAL COMPONENTS............................................................................................ 13

3.5 OPTICAL MANUFACTURING: EB COMPONENTS ............................................................... 15

3.5.1 Radius of curvature............................................................................................. 15

3.5.2 Central thickness & Diameter............................................................................ 16

3.5.3 Surface Irregularity.............................................................................................. 16

3.5.4 Diameter ............................................................................................................... 17

3.5.5 Wedge: ................................................................................................................. 17

3.5.5.1 a) Singlet lenses ............................................................................................17

3.5.5.2 b) Doublets and Triplets: ..............................................................................18

3.5.6 Surface Irregularities .......................................................................................... 19

3.6 GLASS-BLANK COMPONENTS.......................................................................................... 19

3.6.1 Blank Index of Refraction & Abbe number ...................................................... 19

3.6.2 Blank inhomogeneities on refraction index ..................................................... 19

4. ZEMAX MACROS AND ASCII INPUT FILES........................................................ 20

5. TEMPORARY NOTES ................................................................................................ 20

6. SENSITIVITIES RUNS................................................................................................ 21

7. COMPENSATORS CONSIDERED IN THE ERROR-BUDGET MODEL ........... 22

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1. ESOPO ERROR-BUDGET INTRODUCTION

The ESOPO Error-Budget can naturally be constructed organizing the high-level requirements into two groups:

a) Static Requirements, that reflect directly on the design, construction and integration of the instrument, and

b) Dynamic Requirements, which limit the operations degradation of the final system (as constructed) due to flexure changes, temperature variations, mode-change or other after-construction effects.

The error-budget referred by this document relates to most of the ESOPO top-level requirements but not all. Budgets such as for Throughput (including glass transmission and absorption, reflective and antireflection coatings, dispersion and vignette losses) are treated differently and explained in their own documentation.

Most high level requirements of relevance for the optical and mechanical error-budget of ESOPO refer to the actual FWHM spectral resolution together with its variations along the field, and their degradation under explicit changes in operation conditions. These requirements refer to the Final or Actual Resolution and variations, that is the performance the astronomer actually measures directly from his/her data.

In imaging the radial shape of the image on the detector is given essentially by the convolution of the object radial profile, the seeing profile and the instrumental profile:

P(r) = ρ(r) ¤ σ(r) ¤ I(r)

In spectroscopy, the dispersive element (grating) breaks the radial symmetry. One of the coordinate pair in the detector (say x, or rows) still refers to a spatial scale while the second one, along the dispersion direction (say y, or columns), now physically refers to wavelength not space. In spectroscopy, we then must consider two image sizes detected which, due to the grating anamorphism, the chromatism of optical aberrations and distortion, can in general be quite different, and are usually expressed in different units.

Since the grating disperses, at different angle for each wavelength, monochromatic images of the convolution ρ ¤ σ chopped (or multiplied) by the slit aperture (width), the image size along the dispersion, the one that actually gives the spectral resolution, is now dependent on the slit width W. Such that, at the detector:

Px(x, y) = ρ(r) ¤ σ(r) ¤ Ix(x, y) ... Image profile along the slit length (x-rows)

Pλ(x, y) = ((ρ ¤ σ) Wλ) ¤ Iλ(x, y)... Image profile along dispersion (y-columns)

These general case equations show that the actual resolution is a combination of the slit width, the seeing, the light distribution of the source and the Instrumental PSF. When the seeing and source are much smaller than the slit width, the resolution is

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limited by the instrumental resolution, when the source gets extended well beyond the slit-width (either intrinsically or after being smeared by a large seeing) the resolution is now given by the convolution of the projected slit width and the instrumental profile.

For a clear specification, ESOPO was required to achieve its resolution for an extended source homogenously filling the slit width; in this case the second of the above equations takes a simpler form:

Pλ(x , y) = Wλ(x, y) ¤ Iλ(x , y) ... extended-source profile along dispersion

The convolution has the nice feature that any width measure of the convolution (e.g. FWHM) is exactly given by the widths of the intervening functions added in quadrature. Therefore, the spectral resolution will be given by the FWHM of the top-hat slit-width (W) and the FWHM of the instrumental profile (FWHMy):

FWHMλ2 (x, y) = Wλ

2(x, y) + FWHMy2(x, y)……………. Static resolution

The above equation is correct for the Static Error-Budget, but it ignores the resolution degradation due to smearing cause by image motion. For the Dynamic Error-Budget we must then include a third convolution factor, the amount of motion projected along the respective coordinate:

FWHMx2 (x, y) = FWHMx

2(x, y) + ∆x2……………… Spatial resolution

FWHMλ2 (x, y) = Wλ

2(x, y) + FWHMy2(x, y) + ∆y

2…… Spectral resolution

Therefore, all the ESOPO resolution requirements can be quantified directly from measuring on the detector the image size (in-slit FWHM along dispersion), the image location (x, y) and the projected nominal slit-width on the detector (plate-scale) all in the same units. By measuring these three quantities directly in pixel units, one can naturally account for the requirements of both resolution and its sampling at once, and regardless of the different physical pixel sizes of the two arms. The deterioration from a given perturbation can also be quantified by direct comparison of the FWHMs of the reference (unperturbed) and perturbed systems:

∆FWHMλ

2 = ∆Wλ

2 + ∆FWHMy2 + ∆y

2…… Spectral resolution degradation

The three base measurements (image quality, location and slit-width), are computed at each wavelength and field for all of the ESOPO variables tolerated in the Error Budget Tree (tilts, shifts, manufacturing, and other tolerances) for the relevant configurations (gratings, arms, etc) and conditions (gravity, operational temperature, etc).

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After a single or a perturbation set, the changes in image quality, location and actual slit-width (relative to the nominal reference system) are translated into a minimal and homogenous set of 4 Degradation Measures in order to more easily resolve and operate the Error Budget:

1) Convolutive degradation of central spectral resolution;

2) Fractional change of spectral resolution along the slit;

3) Fractional change of the 2D wavelength calibration; and

4) Fractional change of the 2D spatial calibration.

These four degradation measures directly refer to the ESOPO top level requirements, avoiding any other intermediate calculations and minimizing potential errors or ambiguities in their interpretation.

In this way both, the Sensitivities and Error-Budget analysis in ESOPO are managed by the combination of a Zemax file that allows, for all the tolerated perturbations, a pair of Zemax macro files that operate on this file (one for sensitivities and another for error-budget), a set of ASCII files with the input instructions for the Zemax macros and, finally, an Excel Spreadsheet that takes the output of the Zemax macros and translate them into and with the units of each high-level requirement considered in this Error-Budget.

2. ESOPO RESOLUTION REQUIREMENTS

The ESOPO top-level requirements referring explicitly or indirectly to the resolution performance are:

1. ESOPO must be coupled to the f/7.5 focus of the SPM 2.1 m Telescope. 2. The whole spectral range (350-900 nm) must be observable at once, at least at the

minimum resolution (R~300 or higher). 3. A real FHWM spectral resolution R=5000 must be achievable with 1200 ll/mm

grating, with a maximum cross section of 154 x 206mm, and a nominal slit width of 0.8’’.

4. The spectral resolution sampling: from 2.3 to 4.0 pixels per FWHM (0.8” slit). 5. Maximum variation of actual resolution along the slit: less than 10% (goal: <5%). 6. Pupil size limited by the size of commercial (off-shelf) gratings. 7. Slit length: a minimum 8’ field and a goal of 10’. 8. Plate-scale along slit: ≤ 0.5’’/pixel (only if not compromising spectral resolution) 9. CCDs: Blue: 2048x4608 13.5µm pixels; Red: 2048x4096 15.0µm pixels. 10. Repetitiveness and stability such that:

a. Resolution should not degrade by more than 2.5% over 30 min exposures. b. Resolution constant within 5% after changing and coming back to a given

configuration (goal: 3%). c. Relative calibrations at beginning/end of night (relative to spectral

dispersion and resolution, plate scale and responses along slit and spectral directions) should apply to all within-night data with a confidence level

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better than 10% (in relative functional shape, but not in an absolute sense or zero point) under the nocturnal temperature changes (+/-6˚C), flexures or other derivatives (goal: 5%).

11. Design, operation and survival ambient requirements: a. Optimization temperature and atmospheric pressure: T=3˚C; P=562 mmHg. b. Minimum range of operation (fulfilling requirements): from -10˚C to 16˚C

and 545-570 mmHg. c. Minimum survival range: from -16˚C to 34˚C, and from 500 to 1100 mmHg.

2.1 Design considerations

To fulfill requirements 1, 3, 6, 8 and 9 above, the optical design adopted a pupil diameter of 100 mm and a plate scale of 0.45 ars-sec per pixel, for both blue and red arms (see ESOPO Optical Design document for more details). Therefore:

Pupil diameter 100 100

Collimator Focal length 791.5 795.5

Camera focal length 309.4 343.9

Scale along slit

Scale along dispersion

Dispersión A/Px @ 441nm 0.357

Slit Resolution 6986

3. ESOPO ERROR-BUDGET DEFINITIONS AND THE EXCEL SPREADSHEET.

The first of the “ErrorBudget” Excel spreadsheets summarizes how the ESOPO top-level requirements were translated into the static and dynamic Error-Budgets. The actual Error-Budget tree appears explicitly in the different subsequent Sensitivities and Error-Budget sheets. This three is reflected exactly in the ASCII input files for the Zemax macros.

The following subsection summarizes how the relevant performance measures were in practice defined for the quantification of each top-level requirement in the Error-Budget.

3.1 Operational definitions

All of the resolution requirements translate to only three basic performance measures: central resolution, fractional variation of resolution along the slit, and fractional changes

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of the 2D (wavelength and spatial) calibration. Here we describe how in practice we implemented these three performance measures in the ESOPO Error-Budget machinery.

For this, the Zemax Macros measure, for each sampled wavelength and field combination, the image spatial and wavelength location in the detector (CCD x-row and y column), the 1-D FWHM along the slit and along the dispersion (76.2% En-slited Energy Diameters) in pixel units, and the projected slit-width (of the nominal 0.8”) along the dispersion, also in pixel units. These measurements are done first for the nominal (unperturbed) reference system, and after applying each of the perturbation in the ESOPO Error-Budget Tree.

The resolution map of the reference system is then estimated, within the ESOPO Excel sheets, by the combination of the FWHM along the dispersion (λF0)i,j and the effective projected slit width (W0)i,j, at 63 sampled points (9 fields i=1,2…,9; and 7 wavelengths j=1,2,..,7):

2,0

2,0

2,0 )()()( jijiji WFR +≡

λ

Then, for each perturbation in the EB tree, the ESOPO Excel sheets similarly estimate the resolution degradation at each sampled point as:

2,0

2,

2,

2, )()()( jijijiji RWFR −+≡∆

λ

The above equation is appropriate for the Static Error-Budget, since it reflects the net resolution degradation of the image quality both, because of defocus and image-scale changes (even including the effect from image position change), but without including the smearing as the image drifts.

We must include the degradation from the image smearing along the dispersion (the sole drift-component that affects the spectral resolution) when dealing with the Dynamic EB:

2,0,

22,

2,

2, )()()( jijijijiji RyWFR −∆++≡∆

λ

3.1.1 Resolution-measure Definition

As effective resolution we need a measure of the actual FWHM along the dispersion around the field center (central wavelength and central field). Since single-point definition is somewhat unstable or not always a significant measure, the ESOPO resolution is defined as the average FWHM of the five points defined by the three central wavelengths at the central field and the three central fields at the central wavelength.

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3.1.2 Resolution variation along slit and wavelength

To quantify the change in resolution along the slit we measure the peak-to-valley (maximum – minimum) resolution change within the 8´-long slit, relative to the constant-along-slit nominal resolution, with all the sampled wavelengths considered.

3.1.3 Changes in relative wavelength/spatial calibration

The ESOPO top-level requirements limit how much the relative 2-D calibration can change under flexure effects, temperature variations, and after leaving and coming back to a given set-up. Therefore this quality measure only applies to the Dynamic (operations) error-budget and not to Design, Manufacture and Integration (Static EB).

3.2 Slit Effects

In the error budget the motions of the slit and its variations in width and parallelism will be modeled assuming that the ESOPO guiding system will be centering the source continuously on the slit and that the astronomer/operator will maintain the telescope focus. Since the ESOPO field-guiding camera locks to the image reflected on the slit (and the slit-aperture “shadow” or dark profile), it can not distinguish between the motions due to telescope pointing from motions of the ESOPO instrument or of the slit itself. That is, the object will be maintained centered on the slit “shadow” image by changing the telescope pointing, regardless of whether its was the telescope, the instrument or the slit itself that moved relative to the true reference (source on the sky) .

In the Zemax

BEWARE: this assumes that the guiding algorithm of the ESOPO field-acquisition system, takes track of both, a slit mark and an object center, simultaneous and independently (just like an observer’s eye would do).

In this case, the effect of the physical motions of the slit will be modeled by tilting the whole telescope (with instrument) relative to the sky and refocusing the telescope fields. ESOPO Zemax File (Perturbable Optical Design)

3.3 General Description

ESOPO has no other alternative than to accept at least three natural compensators: the Dichroic/Folder mirror, the grating surface and the CCD surface. Therefore, the actual placement and orientation of these three surfaces will be considered as compensators in the Error-Budget, right from the beginning, to minimize or eliminate fine-tuning mechanism in all other components (both for manufacturing and integration phases).

1) The Dichroic/Folder Mirror will be oriented to define only the optical axis up to the grating interface surface (mechanical alignment). For the error-budget, this alignment (compensation) will be applied first, and independently of the other two, at nominal gravity (zenith).

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2) The optical axis of the camera will be oriented with the aid of a mirror on the grating interface surface, without diffractive optics (mechanical alignment), just as for the previous Dichroic/Folder Mirror case.

3) Each grating will need to be aligned individually in both orientations, conic and dispersive directions, as well as its z-location when mounted the first time. The first angle, coupled with the z-position, simply are to guarantee the same optical axis of the camera defined before (they are also only mechanical alignments). The second angle (dispersion direction) will be used to properly center the specific wavelength range of the given grating.

4) For the error budget, we will assume that the CCD is the last surface to be oriented. We will assume that the CCD will be first referred to the surface interface of the dewar, and that this surface will have required degrees of motion (adjustment). The Dewar window will also be previously referred and centered to the same mechanical interface.

These three compensators (Dichroic/Folder surface, grating surface and Dewar interface) are only manufacturing and integration compensators, applied only once in the integration process, and are not dynamic compensators.

3.4 Mechanical components

Interfaces were defined for the main ESOPO subsystems, namely:

ESOPO as a whole (relative to the telescope)

SLIT

FIELD-LENS DOUBLET

FOLDER MIRROR OR DICROIC

COLLIMATOR TRIPLET:

GRATING: Contains a reference surface and the grating itself.

CAMERA TOP BARREL: Contains the two camera doublets D1 and D2 and the 1st camera single lens S1. These are the largest and heaviest optical components in ESOPO.

CAMERA BOTTON BARREL: Contains the 3rd and 4th camera single lenses S3 and S4. DEWAR: Contains the Dewar window and the CCD detector

The following table summarizes the placement of the above subsystem interfaces or reference surfaces. The placement of these reference surfaces is actually arbitrary, so our main criteria were:

1. Placement close to the center of mass of each subsystem 2. For single surface subsystems (like the slit), the reference surface coincides

(except for orientation) with the optical surface. This was changed later. 3. Attempt to place blue and red arm reference surfaces at the same height. This

symmetry is not just cosmetically sound but is an important feature for the

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definition and manufacture of the main mechanical planes of the ESOPO supporting structure by the mechanics team.

4. For an easier disentangle of complexities due to the different relevant planes of the gratings, the mechanical interface was referred considering only the conic mount angle, which is actually the same for all gratings in an arm, and does not depend on wavelength or rule properties, because it considers only the behavior of the slit as a second fold-mirror. Within the grating subsystem, each grating will any way have to be properly oriented within its own cell (once). There is then no need at all to call for fine-tuning mechanisms of the Gratins Subsystem as a whole.

5. At a later moment, after an iteration with the mechanical design team, some interfaces were changed a bit (in particular the slit, grating and barrel 2) to be close or actually the mechanical reference.

Table 1. Interfaces Coordinates

Xg Zg Θy (CCW)

ESOPO 0 0 0°

Slit 0 -75.78 0°

Field Doublet 0 55.35 0°

Fold-Mirror 0 360.00 0°

Collimator Triplet Blue -533.92 13.20 61.2°

Collimator Triplet Red +355.15 63.00 -45.0°

Grating Interface Blue -778.78 -141.85 38.7°

Grating Interface Red +540.38 -147.56 -22.5°

Camera Barrel-1 blue -686.60 +111.20 16.2°

Camera Barrel-1 red +522.45 +110.00 0.00°

Camera Barrel-2 blue -590.50 +441.97 16.2°

Camera Barrel-2 red +522.45 +461.60 0.00°

Dewar Interface Blue -562.60 +538.00 16.2°

Dewar Interface Red +522.45 +625.75 0.00°

The ESOPO Zemax file allows for all, and more, degrees of freedom for the motion of the above subsystems, and their components, present in the error-budget tree. For each subsystem, properly paired coordinate break surfaces were explicitly inserted. Before and after each of the above subsystems, the coordinate breaks are always referred to the Global Coordinate System of ESOPO, so all displacements and rotations from the mechanical group (gravity and thermal modeling) can directly be incorporated as calculated by the FEM software.

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Within a subsystem, motions are now referred to the Local Coordinate System of the ESOPO subsystem in consideration, as defined by the above listed interfaces (table 1).

3.5 Optical manufacturing: EB components

The variables taken into account in the ESOPO Zemax file are:

1. Radius of curvature of all optical surfaces

2. Central thickness (and diameter)

3. Optical residual Wedge

4. Surface irregularities

5. Random (measuring) left over errors of the above (Rc, thickness, wedge and random nature of irregularities)

Other characteristics specified and tolerated by other Error-Budgets of ESOPO, such as Scratch and Dig, Dispersion, Antireflection Coatings, Transmission and Absorption, Throughput, are to be explained in other documents.

3.5.1 Radius of curvature

The radius of curvature is manipulated by the Sensitivities and Error-Budget macros via the SURP (set-surface-property) command. As with Zemax standard tolerances, this command does not change the radius of curvature directly but its inverse, the curvature. To facilitate the engineering work and the Optical Shop orders, the EB macros were written to take as input directly the radius of curvature.

Entries of the input files relative to radius of curvature, simply looks like:

Delta Sur Stat Com COD Par v2 Comp Comments

0.100 27 0 0 -2 0 0 1 FDL1S1 Curv Radius (for shop)

0.005 27 2 0 -2 0 0 1 FDL1S1 Curv Rad (after construction)

The first one is an example of a sample tolerance of 100 micros in the radius of curvature (statistics 0), while the second show how to account for a stochastic (stat=2) after-manufacturing tolerance of 5 microns (i.e. the metrology error). The negative value of COD, is to flag the Zemax macros that the property perturbed (curvature) is actually the inverse of the input tolerance (radius of curvature). Par amd V2 are not used in this case regardless of their input value (zero in this example). The Comp value of 1 is to indicate that the 1st assembling compensator (dicroic/folder) applies to this surface.

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3.5.2 Central thickness & Diameter

The central thickness, like the radius of curvature and most mechanical variables, is also manipulated directly by the Sensitivities and Error-Budget macros via the SURP (set-surface-property) command.

Index of refraction (offset solve, SolveType GO) Abbe number (glass dispersion, glass offset solve)

3.5.3 Surface Irregularity

The ISO 10110-5 norm to specify the Surface Form Tolerances has the form 3/A(B/C) RMSt,i,a < D (all Ø…). For spherical surfaces, we will not be specifying the Saggita error tolerance here (A=-), but the radius of curvature tolerance as explicitly modeled above. We are also skipping the RMS and diameter specifications and specify only Peak-to-Valley irregularities, in fringes at 546.07 nm, over the whole surface without explicit Rotational symmetry requirements. Therefore we will only be specifying the B value in the ISO norm.

To properly model the above Irregularity tolerances (B), The Sensitivity and Error-Budget Zemax macros were programmed to treat the surface irregularities as the “TEZI” command does, using the Standard Zernike Sag surfaces. These standard Zernike “Noll” polynomials differ to the most commonly used “Fringe” (or University of Arizona) Zernike polynomials, not only in the ordering of several high-order terms, but more importantly in the normalization that makes the Noll Zernike amplitudes nicely equal to the RMS amplitude.

To set the B PTV irregularity in fringes, we first transform it to an RMS saggita error in millimeters by multiplying by half the reference wavelength and dividing by a statistical factor of 6.6 (typical Peak-to-valley-to-RMS factor for a normal distribution).

RMS(B) [mm] = 2.73037x10-4 B/6.6

The “piston” -or lowest order term- plays no role on statistical irregularities, so we do not perturb it. The following low-order Zernikes, up to the 8th polynomial (term #7), essentially describe tilt, focus, astigmatism, and coma aberrations, in both, Fringe and Noll Zernike polynomials. The 1st spherical aberration Zernike is term 8 in Fringe and term 11 in Noll polynomials. In our modeling, we assign power up to the 36th Zernike, since higher frequencies are usually depressed during the polishing process.(this highest order can be varied in the input files).

Using the ortho-normalization property of the Standard “Noll” Zernike Polynomials, as the advantage over the Fringe “UA” Zernike Polynomials, we can properly model the total RMS by assigning the same amplitude to all terms given by:

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Ci(B) = RMS(B) / (Nz-1)1/2………………..………...(i=2,3,…,Nz)

For sensitivities, we use either the positive or negative case. For Monte Carlo realizations with peak-or-valley statistics, we randomly assign the plus or minus sign to each term. In the cases of Uniform or Gaussian statistics, the amplitude is randomly chosen for each term (with the given statistics), and afterwards we multiply all terms by a normalization factor that yields the desiderated total RMS:

f = RMS/(Sum(Ci2)1/2

This last Uniform and Gaussian statistics case is a nice feature programmed in our Macros for a realistic modeling of random irregularities, actually not implemented in the Zemax TEZI tolerance.

3.5.4 Diameter

This is not a relevant variable for optical performance and is not considered part of the error-budget. Nevertheless, the ESOPO Zemax file models carefully the behavior of diameter with temperature, in particular to aid on the optomechanical specifications, to calculate blanks at 20°C, and to prepare the manufacturing drawings and specifications for the optical shops (then again at 20°C).

3.5.5 Wedge:

To minimize extra coordinates break surfaces in the ESOPO ZEMAX file, it was decided to model and manipulating wedge with the driving Macros (Sensitivities, Error Budget, etc) changing the Tilt/Decenter tabs values through the SURP command (Set Surface Property command). The relative motions among lenses in multiplets are also controlled in the same way, so be careful on the conventions.

3.5.5.1 a) Singlet lenses

In case of singlets the unperturbed wedge was defined as zero, since it is expected that lenses will be mounted with self-centering techniques. This is also re-enforced by the fact that most singlets in ESOPO require minimal or null radial support, which can prevent or limit self-centering. Of course, the rotation of the lens as a whole due to optomechanics can act as a wedge plus a displacement, but is taken care off by the mechanical EB (further described).

The only singlet where we assume wedge is the Dewar window, since the reference surface is the flat one, and the pressing surface will be a bevel, this mount does not provide a natural self-centering bias.

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3.5.5.2 b) Doublets and Triplets:

Then again, a self-centering mount makes that the first and last surfaces of a singlet or a multiplet lens are centered (no net wedge), so the fabrication wedge ends up showing up as a tilt of the internal surfaces of the multiplet.

An ambiguity appears nevertheless, since the cementing process actually controls the final net wedge of the cemented multiplet, regardless of the wedge of the individual lenses as manufactured. That is to say that it is always possible to cement the lenses by self-centering techniques that reduce or eliminate the lenses wedges, or even to end up with a wedged doublet from non-wedges lenses.

For this reason, in the ESOPO Error-Budget and Sensitivity Analysis we decided to tolerate as wedge ONLY the tilt of the bonded surface pairs of each multiplet. This sets the tolerances not for the manufacture process of each lenses but for the net whole process of lens manufacture and cementing combined. After mounting in ESOPO, motions and tilts of each lens within a multiplet -that can act like an effective wedge- are also tolerated, but through the tolerances in displacement and tilt allowed by the elastic (e.g., O-ring) or elasthomeric (e.g., couplant) of the mounting.

General cementing processes and wedge (just as the sake of discussion):

a) Self-centring Cementing. In this case, the net wedge is in principle zero or negligible and, although the tilts and displacements after mounting can produce a wedge-like effect, wedge of individual lenses does not need to be tolerated for manufacturing since it is compensated (up to a limit) by the bonding process.

b) Edge-aligned Cementing. This is a case in which the multiplet is bonded using as references the lateral (edge) faces of the lenses. In this case, a self-centring mounting in the instrument will yield a net inclination of the internal (bonded) surfaces predicted by the manufacturing wedge of the individual lenses, depending on which of the external surfaces is touching the hard-reference metal surface. Simple geometric arguments can show that in this case, the net inclination of the internal surface of a doublet is given by the manufacturing wedge of the lens not directly touching the reference surface (say W2 if lens1 is the referenced one). The natural extension of this rule for a triplet is such that the fist internal surface pair has an inclination given by W2+W3 and the second (last) internal surface-pair simple W3. In general, for higher order multiplets: Wi=Sum(j+1,N) Wj (j=i,N).

c) Non-controlled Cementing. As mentioned before, in this case the net inclination of internal surfaces due to wedge is not predictable from the manufacturing wedge of the individual lenses, and need only to be measured after bonding. This is the case that we ended up tolerating in the ESOPO Error-Budget.

Operational Notes.

Since the tabs used to tolerate wedge as the coupled tilt of bonded surfaces are the same used to move the 2nd lens respect to the 1st lens, follow these instructions due to the way the ESOPO Zemax file was designed for these effects:

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• For Wedge: Use the “before the surface” Y-tilt (surp surface, code=BTY, value) in the surface that defines the couplant. This tilt will be inherited by the first glass surface of the second lens, and reverted immediately afterwards (without affecting the last surface of the 2nd lens). Use a random value between -90° and 90° (or from 0 to 180°) for the z-tilt to model the unknown orientation of the wedge.

• For the relative motion/tilt of the second lens relative to the first one, use the Tilt/Decenter tab values of the 2nd couplant surface (1st surface of the 2nd lens). These motions/tilts will be inherited also by the last surface of the second lens, and reverted after this last surface. Only x or y displacements are of relevance here (see next point for dz), use the before DecX. Only one of the x-tilt or y-tilt is necessary (use the before Tilt-Y). After the use of the before DecX and TiltY, also use a random before Tilt-Z for the unknown orientation of the x displacement and the y-tilt of the lens.

• For the motion (along z) of one lens to the other, use the thickness of the couplant. This thickness change is reversed after the last surface of the multiplet. Take into account that the thickness change is really a projected z-shift (by the cosine of the wedge angle, and not affected by the angle of the lens tilt described just above).

• Remember that the motions and tilts of one lens in a multiplet, relative to the previous lens, are limited (small) motions restricted by the couplant gap.

3.5.6 Surface Irregularities

3.6 Glass-Blank Components

The specifications to the glass manufacturing companies (Schott, OHara, Richardson Labs, etc) are estimated by including in the Sensitivity and Error-Budget analysis the effects of following properties:

1. Blank index of refraction

2. Blank dispersion (Abbe number)

3. Blank (volume) inhomogeneities in refraction index

3.6.1 Blank Index of Refraction & Abbe number

3.6.2 Blank inhomogeneities on refraction index

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4. ZEMAX MACROS AND ASCII INPUT FILES

Both, sensitivities and error-budget analysis are performed with macros that read basically identical input files. The input file is basically a list, by subsystems, of the parameters of the ESOPO Zemax file to perturb. The general format of the file is as follows:

Most parameters are modified using the very general SURP (setsurfaceproperty) command, which basically operates in all surface parameters except for Solves tah use command SOLVETYPE (for example to tolerate index of refraction and abbe number it is necessary to use the offset solve in the glass type) .

5. TEMPORARY NOTES

There are five files needed to operate the ESOPO Error Budget:

a) The ESOPO Zemax file described in the previous chapter b) The Zemax macro ESOPOSENS, that perturbs the EZOPO Zemax file variables,

independently one another, generating and ASCII output file per subsystem to feed the Error-Budget/Sensitivities Excel spreadsheet (5th file)

c) The Zemax macro ESOPOEB that perturbs the ESOPO Zemax files variables, all at once (coupled) but each according to its own statistics. It generates a single ASCII output file to feed the Error-Budget/Sensitivities Excel spreadsheet (5th file)

d) A proper set of ASCII (text) files that feed the above ESOPOSENS and ESOPOEB macros (e.g. SampleTol.txt)

e) An Excel spreadsheet “ErrorBudget”, that once feed with the results from ESOPOSENS and ESOPOEB translate them into the actual Error-budget tree.

We refer to this file set as “The Machine” to drive the Esopo Error-budget.

Where are we?

1) Have the Excel spreadsheet “ErrorBudget” ready. Its Error-Budget three must

exactly reflect into the ascii files that feed the macros 2) The ESOPO Zemax file is basically ready, except for:

� Program in it variations fore refraction index and dispersion � Program the irregularities modeling (rms, PtV) Idea: use the standard

zernike surface, BUT it seems to be more practical to run it directly from the tolerance data in Zemax rather that by the macros.

� Paco Pregúntale a chapa que es lo que mide en los interferogramas RMS? PTV? Etc. Y en que unidades (lambdas o mm?

3) Have the sensitivities input file basically ready (it was actually run once, but not for all variables). Except for the above. Must revise that it exactly matches the Error-budget tree in the Excel spreadsheet

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4) A preliminary version of the slit sensitivities and its compensation (tel pointing and tel focus) exists but has not been implemented yet. It is complex but may not be of extreme relevance for the EB.

5) We have not written at all the ESOPOEB macro. It will be a not exactly straight forwarded modification of ESOPOSENS. In particular we have top decide how to make the best combination of systematic variables (temperature, flexures) and random ones (measurement uncertainties, etc). Potentially a few MC will do.

6) We have a pretty good idea of most sensitivities, except for the point 2) Need to finish, especially for the shop manufacturing orders.

7) Give the first Error-budget loop

6. SENSITIVITIES RUNS

We first run the Sensitivities Macro, without compensators, to measure the response of the Error-Budget Measure ∆Еj (j=1,4) when applying the perturbations pi on each of the i-th variable of the system one by one and independently of each other. If the perturbation is small, we expect the system to response (degrade) in the linear regime:

),,1;4,3,2,1(,, periijij nijpa L===∆Ε

In order to account for not being in the linear regime of the perturbation, we run the Sensitivity Macro a second time, now scaling the sample tolerances by a given fraction (in our case a factor of a half). The three points (zero, halved and full sample tolerance) allows a quadratic characterization of the sensitivities:

),,1;4,3,2,1()/()/( 20,0,, periijiijij nijppbppa L==+=∆Ε

Going beyond the linear model, we can more securely use a unique Sensitivity table, all along the error-budget process.

The next table summarizes the such derived sensitivity parameters for all the nper entries in the Error-Budget tree (column XX and XX) of each of the four Error-Budget measures: the convolutive degradation of the central resolution (j=1, column XX) in pixel units, the fractional change in resolution along the slit (j=2, column XX), the fractional error in the wavelength calibration (column xx) and the fractional error of the spatial calibration. In general, the shift perturbations are normalized to units of P0=0.1 mm (100 micros), while the tilt and wedge perturbations to units of one hundred of a degree (P0=0.6 arc min). The perturbations in radius of curvature and thickness are also in tenths of mm (P0=100 microns). The inhomogeneities in index of refraction are in units of P0=10-5 (one in a hundred thousand), the perturbations in index of refractions, while the surface

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irregularities are normalized to a Peak-to –Valley of 0.25 fringes (λ/4). For the rest of the perturbations the normalization factor P0 is also listed (column XX).

7. COMPENSATORS CONSIDERED IN THE ERROR-BUDGET MODEL

The next table summarizes the compensators already considered and programmed to operate in the Zemax, macros and Excel files.

We : Design Compensators, Manufacture Compensators, Integration Compensators and Operation Compensators, as well as their different combinations. Examples of design compensators are melt-data optimization and iterative construction re-optimization. Among purely Integration compensator we can mention the fine-tuning positioning of the Dichroic/Folder mirror, the Grating or the Dewar

Code Property Adjusted Surf

n

Zemax

Variable

Store

Index

Notes

Telescope Guiding -1 TelescopeTilt-x 2 parm(3,n) -

-1 TelescopeTilt-y 2 parm(4,n) -

Telescope Focus -1 M1-M2 distance 4 thic(4) 0

I + O

Dic/FM Integration 1 Mirror local Z 36 thic(n) 3

1 Mirror local Tilt-x 36 parm(3,n) 4

1 Mirror local Tilt-y 36 parm(4,n) 5

I + O

Grating Integration 2 Grating local Z 61 thic(n) 6

2 Grat local Tilt-x 61 parm(3,n) 7

2 Grat local Tilt-y 61 parm(4,n) 8

Grove orientation 2 Grat surf Tilt-z 62 spro( n,65) 9

I

Dewar Integration 3 Dew local Z 110 thic(n) 10

3 Dew local X 110 parm(1,n) 11

3 Dew local Y 110 parm(2,n) 12

3 Dew local Tilt-x 110 parm(3,n) 13

3 Dew local Tilt-y 110 parm(4,n) 14

3 Dew local Tilt-z 110 parm(5,n) 15

I

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FD/CT Cells 4 FD local Z 25 thic(n) 16 IterD

4 CT local Z 43 thic(n) 17 IterD

Collimator Cell 5 CT local Z 43 thic(n) 17 IterD

Camera Cells 6 D1 local Z 69 thic(n) 18 IterD

6 D2 local Z 78 thic(n) 19

6 S1 local Z 87 thic(n) 20



Camera IterConstr - D1L1S1 Rad Cur 72 radi(n) 23 IterD

7 D1L2S2 Rad Cur 76 radi(n) 24

- D2L2S1 Rad Cur 81 radi(n) 25

- D2L2S2 Rad Cur 85 radi(n) 26

- S1S1 Rad Cur 89 radi(n) 27


7 S2S1 Rad Cur 98 radi(n) 29


7 S3S1 Rad Cur 108 radi(n) 31

7 S3S2 RadCur 109 radi(n) 32

Camera Thermal 9

Notes 1. When the Dewar window position is not varied in the Iterative-design

compensation, the Dewar integration does not completely compensate for the curvature radius of the Dewar Window, and actually should not be used (see next note). The Curvature and Thickness of the DW should be compensated together with the rest of the camera lenses, by applying the Iterative-design compensators (6 or 7) after and not before the window.

2. For optical-shop manufacturing tolerances of Radius of Curvature and Lens Thickness, applied only the Iterative-design compensators. The Integration compensations of Dichroic/Folder mirror, Grating and Dewar apply for the measuring errors on Rcur and Lens Thickness where, by the complementary contrast, the Iterative-design compensators do not apply.

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3. BEWARE for the Iterative-Design compensator 4 (Field-doublet/Collimator-triplet distances) both arms must be optimized at the same time, since it varies the position of the field-doublet.

4. The Iterative-Design compensator 8 was defined after running the optical Static EB a first time. Especially the red arm, collimation is very sensitive to the loose tolerance of the long-radius CTL1S1 surface. BEWARE: Since this compensator optimizes the last three surface radii of the triplet, it should be applied before the tolerance and the measuring errors of these radii.

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