DOI 10.1007/s10686-009-9172-7 SHORT COMMUNICATION High-precision CTE measurement of aluminum-alloys for cryogenic astronomical instrumentation I. Mochi S. Gennari E. Oliva C. Baffa V. Biliotti G. Falcini E. Giani G. Marcucci M. Sozzi L. Origlia E. Rossetti M. Gonzalez Received: 12 February 2009 / Accepted: 7 May 2009 Springer Science + Business Media B.V. 2009 Abstract We are completing the construction of GIANO, a high resolution near-infrared cryogenic spectrograph for the Telescopio Nazionale Galileo (TNG). Most of the optics are made of aluminium and operate at cryogenic temperature. We evaluated the optical degradation due to mis-matches between the thermal expansion coefficients of the different aluminium parts of the instrument. We performed accurate measurements of the relative thermal expansion coefficients (CTE) of Al-6061 and Al-6082 over the 300 77 K temperatures range. We find that the two alloys have identical thermal expansion coefficient within a maximum (3σ ) uncertainty of α/α < 0.28%. Our results show that it is possible to overcome the problem of the alignment of a cryogenic instrument, manufacturing the curved optics, the optics holders and the optical bench with different metallic alloys with small CTE mismatch (Al-6061 and Al-6082). This conclusion has also been confirmed by the results I. Mochi (B) S. Gennari E. Oliva C. Baffa V. Biliotti G. Falcini E. Giani G. Marcucci M. Sozzi Osservatorio Astrofisico di Arcetri, INAF, Largo E. Fermi 5, 50125 Firenze, Italy e-mail: imochi@lbl.gov E. Oliva e-mail: oliva@arcetri.astro.it L. Origlia E. Rossetti Osservatorio di Bologna, INAF, via Ranzani 1, 40127 Bologna, Italy M. Gonzalez Telescopio Nazionale Galileo, INAF, P.O. Box 565, 38700 Santa Cruz de La Palma, Spain Present Address: I. Mochi Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA
of the optical tests with the instrument cooled in the laboratory, showing no significant image quality degradation. Keywords Instrumentation Infrared spectroscopy Materials Cryogenics 1 Introduction Aluminum and its alloys are largely employed in areospace industry and cryogenic infrared instruments, being durable, lightweight, easily machined and corrosion resistant. Of particular interests are the Al-6061 and the Al-6082 alloys, both of which have thermal expansion coefficients (CTE) 23.6 10 6 K 1 at room temperature. The CTE of Al-6061 over the temperature range 293 K 77 K is 18.5 10 6 K 1, although, to the best of our knowledge, nothing is known about the accuracy on these parameters, nor on the CTE of Al-6082 between room and cryogenic temperature. For many applications, the Al-6061 alloy is the worldwide standard. However, the European market favours the Al-6082 alloy which has several practical advantages on its quasi-twin Al-6061, that cannot be easily found at a reasonable cost. In the recent years, our group has been involved in the construction of GIANO, a cross-dispersed IR spectrometer covering most of the 0.9 2.5 μm range in a single shot with high resolving power (λ/ λ 5 10 4 ), high optical efficiency and quality. The instrument will be mounted on the Italian telescope TNG in La Palma [6 8]. The GIANO project has been entirely financed by the Italian Institute of Astrophysics (INAF) and it is near completion. The core of the GIANO spectrometer consists of a three mirrors anagstigmat (TMA) system which is used in double pass, first to create a 100 mm collimated beam feeding an echelle grating through prism cross-dispersers, and then to focus the spectrum on a 2K x 2K detector (see Fig. 1 and [2]). The TMA system is composed by three off-axis conical mirrors (TMA1-3 in Fig. 1) manufactured from aluminium 6061 alloy. Two other conical mirrors (FR1-2 in Fig. 1) of the same material are used as slit-relay and focal adapter. The mirrors Fig. 1 Optical layout and ray tracing of the GIANO high resolution infrared spectrometer. The aluminium mirrors are FR1-2 and TMA1-3
are mounted on an aluminium optical bench, which also acts as liquid nitrogen tank [3, 4]. The optical bench has a a size of about 130 100 25 cm, and it has been machined out of a single block of Al 6082 by the Italian company Criotec Impianti s.r.l. (see http://www.criotec.com/). The system was aligned at room temperature (T 295 K) using the technique described in [5] and operates at cryogenic temperature (T 77 K). The relative alignment between the mirrors is maintained if the mirrors reach the same temperature of the optical bench because they are made of materials with the same thermal expansion coefficients. Hence, two fundamental laboratory tests that have been performed within GIANO project, namely 1) the relative variation of thermal expansion coefficients of Al-6061 and Al-6082 between room temperature and 77 K, and 2) the effect of CTE-variations on the optical quality of the GIANO-TNG spectrometer. This paper reports the results of our tests, as presented and discussed in Sections 2, 3 and 4. 2 Measurement of the CTE for Al-6061 and Al-6082 The first simple test consists of measuring, by means of a dial indicator, 1 the difference of length dl between two bars of equal lengths L when they are immersed in liquid nitrogen (see Fig. 2). The value of dl is related to α, the difference of the CTE s of the two materials, by: dl = L α T ; α T = dl L (1) where T is the difference between ambient and liquid nitrogen temperatures (about 200 K). Two bars with L = 250 mm were used and no displacement was detected within the limits of the dial indicator, i.e. dl < 0.01 mm, hence α T < 4 10 5.Sinceα T 4 10 3, the corresponding upper limit for the relative variation of CTE is α/α < 1%. The second, more accurate measurement consists of welding two relatively (several mm) thin bars of the two alloys and measuring the variation of dl,the height of the central part relative to the edges (see left panel of Fig. 2). This was performed by positioning a dial indicator in the center of the bar while holding the bar edges with two steel bands. The bar was laid on a plate of Al- 6082 and the dial indicator was secured to the same plate. The displacement dl was determined by measuring the variation of the dial indicator between room and liquid N 2 temperatures. If the CTE of the two alloys were different the two bars would bend upward or downward creating an arc shape like the one shown in the left panel of Fig. 2 where the curvature center is on the side of the material with the higher CTE. Note that if the bar facing down has the lower CTE, the two bars would bend raising the edges and the middle point would not move. 1 The dial indicator was previously tested and found to work properly even when immersed in liquid nitrogen.
Fig. 2 Sketch of the two setups used for the measurement of differential thermal expansion The measurements, which were repeated many times, also turning the bars upside down, showed no significant difference between the two alloys. The upper limit of the displacement was estimated as: dl < 0.015 mm. It is worthwhile noting that minor deflections might have been induced by stress relief caused by the welding, but they are below the sensitivity of our measurement. The deflection can be related to α as follows (see e.g. [1]). k = 6E 1 E 1 (t 1 + t 2 )t 1 t 2 α T E 2 1 t4 1 + 4E 1E 2 t 3 1 t 2 + 6E 1 E 2 t 2 1 t2 2 + 4E 1E 2 t 1 t 3 2 + E2 2 t4 2 (2) where k is the measured curvature of the double bar, t 1 and t 2 are the thicknesses of the two bars and E 1, E 2 are their Young s moduli. Since E 1 E 2 and t 1 = t 2 = t the above equation reduces to k = 3 α T 4t (3) The expression for dl follows from simple geometric considerations R = 4t 3 α T ; θ = L ( R ; dl = R 1 cos θ ) 2 (4) where R is the curvature radius of the bar and L is the length of the bar. Taking into account that θ<<1 one finds dl = 3L2 α T 32t ; α T = dl L 32t 3L (5) The comparison between Eqs. 1 and 5 indicates that the sensitivity of the measurement is amplified by a factor 3L/32t, wherel is the length and t is the thickness of each bar. We used two bars with L = 269 mm and t = 5 mm, hence the amplification factor was equal to 5.
Given the measured 3σ upper limit of dl < 0.015 mm, the corresponding upper limits on the difference of thermal expansion coefficients is α/α < 0.28% (6) α T < 1.1 10 5 (7) α < 5.4 10 8 K 1 (8) 3 The effect of CTE variations on the optical quality The optical quality of the spectrometer is defined by means of the encircled energy within 18 18 μm (the pixel size) measured at different positions of the echellogram. To evaluate the effect of using materials with different thermal expansion coefficients for the mirrors and for the bench we modified the optical model varying the curvature radii of the mirrors by a factor (1 α 1 T) and the distances between the mirrors by a factor (1 α 2 T), where α 1 and α 2 are the thermal expansion coefficients of the Al-alloys used for the mirrors and for the bench, respectively. The parameter T is the temperature difference between room and cryogenic conditions. In the computation we adopted α T = 410 3, a typical value for aluminum, and varied (α 2 α 1 )/α = α/α between 0% (i.e. ideal case of perfectly matched alloys) to 2%. The results of the simulations, carried out with Code-V, are displayed in Fig. 3 and indicate that CTE mismatches of up to 0.5% have virtually no effect on the optical quality of the system. Values as large as 1%, or even 2%, could also be Fig. 3 Energy falling within a 18 18 μm pixel at various positions of the array as a function of the relative variation of the CTE of the Al-alloys used for the mirror and for the bench. The points displayed are the average between the values measured inside each order. Note that order 32 corresponds to rays travelling with the minimum off-axis angle inside the TMA system, while order 83 corresponds to maximum off-axis angles
T=295 K T=77K order #123 order #122 order #121 _ Detector focus + Fig. 4 Intra and extra focal images of a monochromatic HeNe 633 nm laser source seen at different orders on the focal plane of the GIANO spectrometer. The two panels show the images recorded at room and liquid nitrogen temperatures. The mechanical focal positions are the same in both cases, i.e. the best focus position does not shift with temperature. The higher noise in the images taken at room temperature is an intrinsic characteristic of the Hawaii-II MUX used as detector accepted as they only produce a small deterioration of the image quality on the bluest edge of the spectrum, i.e. on the rays traveling with the largest offaxis inside the TMA system. 4 Optical tests at cryogenic temperatures The alignment of the GIANO optics was performed at room temperature using intra and extra-focal images from a monochromatic HeNe 633 nm laser source which illuminates the entrance slit of the spectrometer (for more details see [5]). The same analysis was used to verify if the system remains aligned at cryogenic temperatures. The results shown in Fig. 4 demonstrate that the image quality does not deteriorate and the focus position does not vary when the spectrometer is cooled. This confirms that optics, holders and bench can be equally well manufactured in Al-6061 or Al-6082, without affecting the optical quality of the cryogenic instrument. 5 Conclusions As a part of the development of GIANO-TNG, a high resolution nearinfrared cryogenic spectrograph with optics based on aluminum mirrors, we have evaluated the optical degradation due to CTE mis-matches and temperature variations between the different aluminum parts of the instrument. We found that variations as large as (CTE)/CTE = 0.5%, or equivalently T/T = 0.5%, have virtually no influence on the overall image quality. We also measured the relative values of CTE s for the Al-6061 and Al-6082 alloys down to 77 K. We found that they are identical within a maximum (3σ ) error
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