SDN 0003.23 – GNIRS Filter Properties

1. Introduction 

This note contains several sections below. The first summarizes the basic mechanical properties and mount design of the filters. The second discusses mechanical and optical properties of the filters as delivered (and will change to the extent filters are redone). The final section is a summary, which includes additional work needed (if any). A spreadsheet containing all of the measurements and calculations is available but is not included in the SDN.

 Revision A consists of inclusion of data for all filters delivered to date.

Revision B adds data for sorter 2, plus a revision of the discussion on machining filter seats.

 Readers uninterested in the details should skip to section 4.

 2. Mechanical Properties

 2.1 Filter Dimensions

 2.1.1 Thickness

 The GNIRS filters precede the slit in order to minimize the effects of ghost images. However, in this geometry (converging beam) differences in filter thickness lead to differences in focus. Although in principle small differences in focus could be corrected by changing telescope focus via the wavefront sensor(s), there is in fact no provision in the interfaces for doing so. Therefore, all filters must be of constant optical thickness. This implies a physical thickness, T, given by

 T = t₀ * n/(n - 1)

 where n is the refractive index of the filter substrate at the wavelength of the filter, and t₀ is the "optical" thickness, which must be the same for all filters. An additional correction could be made for the coatings on one or both sides of the filter, but the thickness of these layers is small compared to the substrate thickness variations.

 The index is a function of wavelength, so that even if the same material is used for all filters the nominal substrate thickness is not the same. However, for thin substrates the differences are small enough that a standard substrate thickness does not introduce significant defocus.

 For the GNIRS filters, a value of t₀ of ~1 mm was adopted, with the resulting design thickness values given below:

Filter Design Parameters

 The allowable thickness variation (according to Ming’s tolerance analysis, 5/26/97) is ±0.040 mm for the low index substrates – so a uniform BK-7 (filters below 3 mm) substrate thickness of 3.00 mm is within tolerance. Of course, the variations in substrate thickness can make things worse, if a long wavelength filter is undersize or a short wavelength filter is oversize.

 Although the thickest filter in the current set would be ~3.04 mm (0.120 in), it is possible for future filters to be somewhat thicker. About the worst (plausible) case in terms of thickness would be a “clear” filter out of CaF₂ intended for longer wavelengths, which would have a thickness of 3.50 mm (0.138 in). The filter wheel must be designed to accommodate filters of up to this thickness (and as little as 1.40 mm (0.055 in) – see table above). Earlier specifications called for a maximum thickness of 8 mm, but this is no longer a requirement given the optical thickness adopted by the vendor.

 2.1.2 Length and Width

 The final filter dimensions are set to 32 x 78 mm (1.260 x 3.070 in). Tolerances on the drawing sent to IR Engineering were ±0.010 in (0.25 mm). The delivered filters have been checked and the results are summarized below.

 Filter Dimensions (Inches)

 In designing the mounts for the filters, it is necessary to make allowance for the differences in thermal contraction down to 60K. A number of filter substrate materials contract only minimally, so the aluminum filter “seat” must be made oversized to allow for its contraction (0.408%). The dimensions given above do not include any machining tolerances; these must be added. The values given first are the maximum measured values plus the allowance for contraction, while the values given in parentheses are the nominal values plus the allowed substrate tolerance plus the allowance for contraction. These (latter) values will accommodate future filters as well as those we now have.

 2.2 Filter Mounting

 The filters are to be mounted at an angle, in order to shift ghost images off-axis (at least for bright point sources). The angle adopted is 2.8 degrees. The tilt shifts the optical axis by an amount that is the same for all filters, and is given by

 Dx = t₀ * q

 For the design parameters, Dx = 0.049 mm (0.002 in). Note that both variations in thickness and variations in tilt produce a displacement of the object on the slit.

 A simple and acceptable approach to putting the filters in their seats is to use a Delrin spacer (or equivalent) between the filter and its seat, and then to put another spacer on top of the filter and use a spring to hold the filter in place. The spring pressure should be sufficient to hold the filter in place against gravity, including sliding sideways. Since the filter weight is under an ounce [< 30 g], a fairly weak spring should suffice.

 The tolerances on the filter seats and Delrin spacer are not very demanding. The quoted tolerances on 0.01 – 0.02 in thickness Delrin strip is ±0.0025 in (0.062 mm). Since the spacer will have some width, the thickness variation should be applied to a dimension somewhat shorter than the full filter width or length. Adopting a value 10 mm less, and assuming that the thickness tolerance quoted above applies from one side of the strip to the other (which is probably pessimistic), the angular tolerance in filter tilt comes out as 2.9 mrad in tilt about the slit axis and 0.9 mrad in tilt about the dispersion axis, which lead to displacements perpendicular to and along the slit of 2.9 and 0.9 mm, respectively. If a similar tolerance is applied to the machined seat the total effect is roughly doubled. Note that the critical machining tolerance is the difference between one filter seat and the next, and not the tolerance on the absolute tilt angle.

 In the final design, the filter tilts are achieved by mounting the filter wheel assembly at the required angle, rather than machining tilted filter seats. This means that any variation in tilt angle will be due to eccentricities in the filter wheel and its mount, which should be well within the above requirements.

 3. Real Filter Properties

 3.1 Flatness Measurements

 The filters as delivered are not ideal. This document does not consider optical defects such as red leaks or pinholes. In this section, the effects of substrates that are not perfectly flat are discussed.

 Measurements of the filters were made in the NOAO Optics Shop, and are summarized in the table below. Nine points on each filter were measured. From these measurements, several quantities were determined:

 ·        Thickness

·        Wedge in X (across width of filter)

·        Wedge in Y (along length of filter)

·        Power (equivalent radius of “lens”)

·        Residuals

 The internal consistency of the data indicates that the measurements themselves are good to about 0.001 mm.

 Filter Measurements

 The first of the two tables summarizes wedge, thickness, and power effects. Usually, the wedge angle is greatest across the thin dimension of the filters.

 The measurements show variations in thickness that are consistent with the substrates acting like weak spherical lenses. It is not possible to tell whether this is due to one or both surfaces – and since the “lens” is both weak and thin, it doesn’t matter. All of the focal lengths are >100 m, and in some cases effectively infinite. However, as discussed below, the effects are not completely negligible.

 The residuals shown take into account the fact that the fit has four degrees of freedom. For those cases where the residuals are ~1 mm, it is reasonable to assume that the filter is described well by the properties tabulated. For those where the residuals are larger (note especially BB2a) the filter is not so well described, and the image quality will be worse than that predicted below.

 3.2 Effects of Flatness Errors

 The filter wedge will have two effects because the beam is being deviated. First, the re-imaging of the Offner cold stop on the spectrograph pupil (at the gratings) will be shifted slightly. For the worst case, the deviation in the beam that is produced is about 0.18 mrad (the wedge angle times n-­1).  This results in a shift at the grating of about ¼ mm (0.01 in), which is likely to be undetectable.

 Second, there is a shift of the object at the slit. For a filter in the front filter wheel (distance to slit = 104 mm) the resulting shift at the slit is 18 mm; for a filter in the second filter wheel (distance to slit = 82 mm) the shift is 15 mm. This is larger than the allowable error budget (about 10 mm), and if filters with wedge this large are used, it will be necessary to shift the slit to compensate.  This would affect the spectrum zero point on the array, but since the effect will be small (and consistent) this is not important. The effect along the slit is smaller, but not entirely negligible. It will be necessary to carefully calibrate the scale and zero-point along the slit for those observations where precise positional registration from one waveband to another is required.

 Filters whose thickness is different from the specified value will also have shifts in X (cross-slit) because they are tilted; these tend to be smaller.

 The X and Y shifts for the individual filters are tabulated below. Note that since the filters can be flipped in both X and Y, it is possible to orient the wedge angles so that the shifts are all in the same sense, which would halve the range of the shifts. The calculations assume that all filters are in the second filter wheel (closer to the slit).

 Filter Thickness Residuals