A.

Optical layout

The optics of PILOT have been designed in order to provide a large instantaneous field of view of about 0.8°x1°, an equivalent focal distance of 1800 mm and a F/2.5 numerical aperture. Its angular resolution is better than 3.5 arcminutes at 500 microns. Its optical layout is shown on Fig.2. It combines a large primary mirror (M1) and a cooled Photometer at 3K including the cold optics. It consists of three optical subsystems: telescope, re-imager and polarimeter [2].

Figure 2.

Optic Layout of PILOT.

The telescope is an off-axis Gregorian telescope. It is composed mainly of an off-axis paraboloid mirror M1 with a large diameter and an off-axis ellipsoid mirror M2, in order to avoid central obscuration. Both mirrors are made of Aluminum. Their off-axis distances, tilt angles and focal distances are combined to satisfy the Mizugushi-Dragone condition [3], and form an equivalent on-axis parabola to minimize instrumental polarization effects.

The reimaging optics consists of two polypropylene lenses forming a telecentric objective. The first lens L1 is at the telescope focal plane, it images the primary mirror onto the cold Aperture stop; the second lens L2 images the telescope focal plane onto the detectors.

A flat mirror M3 is used to fold the beam to reduce the Phtometer volume.

The polarimeter consists of a rotating Half WavePlate (HWP) and a fixed polarizer. The HWP is placed near the cold stop and is motorized in rotation to change the polarization direction of incoming fields.

The half wave-plate is made of sapphire with five thin plates designed for the dual spectral bands 240 μm and 550 μm [4].

Concerning the rejection of the straylight (coming from the ground, balloon, and the emission and diffraction of warm objects), there are two stops in the photometer: one is a Field Stop at the telescope focal plane, with a similar form of the detector array plane; and the other is an cold Aperture Stop, located between the two lenses.

All optical elements except the primary mirror constitute the cold optics, and are located in a 3K cryostat.

This optical configuration is optimized to provide a diffraction limited image quality all over the large focal plane and to minimize straylight.

B.

Subsystem Characterization

The primary mirror is an off-axis parabola with a diameter of 980 mm. Its optical parameters were measured using a 3D machine and verified by optical measurement, including surface curvature, conic constant, off-axis distance. Its characterization was performed on a dedicated optical bench, used for ODIN telescope; the details are described in [5].

The secondary mirror is an off-axis elliptical mirror with 200 mm diameter; it plays a critical role in combining the M1 into the Photometer by its two focus. We need to check and align M2 and M3 by classical optical means at visible wavelength. M2 is made of aluminum and manufactured by numerical diamond machining. Its surface is of optical quality with a surface accuracy of 0.3 μm in P-V, and the roughness of 10 nm in RMS.

Its optical surface parameters were measured with a 3D machine and checked with a Point Diffraction Interferometer. Fig.3 shows the optical test bench. It composed of a He-Ne laser, a microscope objective, a pinhole, the mirror M2 under tested and a reflective ball. The pinhole and the ball are placed at the ellipsoid mirror M2’s two focus position respectively. A beam splitter, placed between M2 and the ball, extracts a part of the beam and send to the PDI interferometer. Fig.4 the interference pictures obtained. The middle picture shows the almost perfect interference picture when the secondary focus was at the right position; and the left and the right pictures show the ones for defocused positions.

Figure 3.

Picture of the optical test bench.

Figure 4.

The obtained interference pictures.

The two refractive lenses, L1 and L2, are made of polymer. Some polymers present non-homogeneous characteristics depending on their manufacturing process.

The knowledge of the optical properties of the material is of great importance to the instrument polarization performance. We developed an optical bench to characterizing the polarization effects of materials and tested three different polymer materials: polypropylene, polyethylene HDPE, and UHMW. The results showed that the polypropylene samples (three samples cut from three orthogonal axes) presented non-obvious polarization effects. But this was not the case for other two materials. So we choose polypropylene for the lenses and windows material.

We measured the polypropylene refractive index, its transmission and thermo-elastic parameter both at room temperature and at cryonic temperature.

The obtained refractive index values are 1.500±0.004 at room temperature, and 1.524±0.006 at 4K.

The transmission was measured with 2 mm and 10 mm thickness samples, and the obtained values are 0.865±0.004 and 0.649±0.002 respectively.

The thermal expansion factor was measured with 2 mm thickness sample at room temperature and at 77K; we obtained the total contraction is 1.14%, which is concordant to the value of 1.15% at 80K described in [6]. So we take 1.25% for 4K as in [6].

The lenses were manufactured using a 3D cutting tool and their surface parameters were obtained by fitting the data measured using a 3D machine.

All the realistic optical and thermo-elastic parameters of the optical elements are taken into account in our optical simulation, thermo-elastic analysis and alignment procedure.

C.

Optical Alignment

The requirement on the overall optical quality of the PILOT instrument translates into the alignment between the primary mirror and the photometer and leads to a required accuracy of about 300μm for the focus relative positions, and a maximum mismatch of 0.06° for their optical axes orientations. This requirement must be satisfied at all time during the observations at ceiling altitude, while the elevation of the pointed load is changed and the temperature of the structure evolves producing thermo-elastic deformation. This is actually one of the most stringent requirements for the experiment.

Fulfilling this requirement has implied a series of actions: First, precise characterizations of the mechanical and optical properties of the primary mirror and of the photometer have been carried out separately. The mirror characterization was performed using a submillimeter test bench. The photometer optical characteristics were determined using ZEMAX simulations, together with optical and 3D measurements. Second, specific tools and an efficient procedure have been developed to align the two subsystems, both for ground test and before flight. To perform this alignment, the primary mirror is mounted on a hexapod, which allows six degrees of freedom for the adjustment while maintaining the stiffness of the system. A numerical model of this mechanism allows a fast convergence of the optical alignment. The relative position of the two subsystems is checked by measuring, using a laser tracker system, a series of optical reference balls associated with the mirror and the photometer. Third, despite the fact that the whole structure connecting the photometer and M1, and the M1 mirror itself are made of the same material (aluminum), which limits differential dilatation, the optical system is off-axis and no perfect compensation of thermo-elastic effects is possible. In order to control the optical alignment during flight, a thermal model of the instrument has been developed. Before launch, the use of this model, knowing the temperature during flight, will allow us to correct for the expected displacement, compensating to first order the effect of the thermal expansion of the mechanical structure expected at ceiling altitude. Fourth, deformations of the holding structure due to gravity at the various elevations have been modeled using a finite element analysis based on Nastran. These deformations are expected to be somewhat lower than thermal deformations. They have also been measured during tests.

D.

Photometer Spectral characterization

The fine knowledge of the instrument spectral response is important for the determination of both the effective wavelength and the polarization parameters of the measurement. Spectral band mismatch between the two polarized focal planes can induce systematic errors in the polarization properties determination. Indeed, we use two sets of bandpass filters at 240 μm for the transmission channel and for the reflection channel respectively. Therefore a precise spectral calibration of the two focal plane arrays is required.

The optical bench developed for the spectral test and calibration is based on a Martin-Puplett type Fourier transform spectrometer (FTS). This method was successfully used for the Planck/HFI spectral calibration [7]. This bench (Fig. 5) allowed characterizing the overall spectral response of the instrument.

Figure 5.

Left: test optical bench. Right: Spectral response for HWP at 1, 3 and 5 positions for one of the arrays.

The characterization was performed for two polarized beams coming from the FTS and for all angular positions of the half-wave plate. Fig.5. shows the measured spectral response for 3 HWP positions (positions 1, 3 and 5) on one of the arrays [8].

A.

PSF characterization

At 240μm, the Point Spread Function (PSF) is not Nyquist-sampled, so we used a microscan technique to obtain an over-resolved PSF with higher signal to noise ratio. The microscanning consists in a sub-pixel scan of the point source on the focal plane, with a step of 1/10^th pixel. We fitted every image with 2D Gaussian function and we added them up, so as to obtain an experimental PSF that can be compared with the simulated PSFs.

An example of the observed PILOT PSF images is represented in Fig. 7. It shows the PSF images obtained from a microscaning around the pixel (3, 7) of array 6 and array 4, and the comparison between the observed and modeled PSF.

Figure 7.

PSF Images on the focal plane. (a): Measured PSF images around a pixel on array #6 and array #4. (b): The corresponding PSF images obtained by simulation taking into account the collimator property.

The left and right parts of the figure show the Transmission and Reflection detector arrays respectively. We see PSF images are on the transmission array #6 and the reflection array #4 and notice good symmetry between the transmission and the reflection detector arrays.

Fig. 7 (a) presents the obtained PSF images during the tests and Fig. 7 (b) presents the PSF images obtained by simulation taking into account the realistic collimator properties. The intensity is normalized and in log scale. The cross patterns around the PSF in low intensity are on all PSF images. They are du to the diffraction of the four struts structure; which support the secondary mirror of the collimator.

Fig. 8 shows the obtained and modeled PSF images around the pixel (3, 7) of array #6, and the comparison between the observed and modeled PSF along horizontal and vertical cuts. The observed PSF shows reasonably good agreement with the modeled PSF. The simulations include the realistic source hole dimension and the collimator internal structure, but are computed at a single wavelength. For a better comparison, we will compute the equivalent PSF corresponding to the spectral band transmission of the measurements.

Figure 8.

Left: The measured and modeled PSF Images. The intensity is normalized and the dimension of the images is 4*4 pixels. The measured one is obtained from a microscaning pattern around pixel (3, 7) of array #6., the contour levels are at 1.0, 0.5, 0.1, 0.01, and 0.001. Right: profiles along a horizontal and vertical cut. The measured and modeled PSF cuts shown in black and orange respectively.

B.

Defocus

In order to determine the best optical alignment of M1 with respect to the photometer, we have performed a series of defocusing along three orthogonal axes, around the best theoretical focus provided by the Zemax model.

The Z defocusing direction corresponds to the optical axis of the photometer while X and Y are orthogonal to it. To estimate the impact of defocusing on the optical performance, all three axis of the focal plane have been explored with the collimator within typically ±0.8 mm for X, Y axis, and ±1.6mm for Z axis. Then the source PSF was fitted in the obtained images, in order to measure the changes in the Full Width of Half Maximum (FWHM) and encircled energy as a function of defocusing distance. The best focus position was determined as the position of minimum FWHM.

Fig. 9 shows an example of the FWHM variation of the PSF at a given position of the focal plane; the defocus offset distance measured from the initial position. The defocus effect in Z-axis is more important than those in X and Y-axis. The variation of FWHM in function of Z defocus is close to a parabolic function; it allowed us to determine the best alignment position.

Figure 9.

Measured FWHM of the collimator source, as a function of the defocus distance along the X (left), Y (center) and Z (right) on PILOT array #2. FWHM values are in array pixel units, and the defocus is in mm. The horizontal dashed lines show the diffraction limit of the instrument. Blue lines show the FWHM along the X-axis and Cyan lines show the FWHM along the Y-axis. The red lines show the average FWHM over the X and Y-axis and green lines show the FWHM values derived from a circular profile of the PSF.

C.

Polarisation

In order to characterize the polarization performance of the instrument, we have used a large (1×1m) polarizer, developed originally for the Archeops balloon-born experiment, hereafter referred to as ArchPol. The ArchPol polarizer is composed of an array of 3×3 frames hosting a large number of metal wires (50 μm thickness, 100 μm separation) and was initially optimized for millimeter wavelengths. The polarizer is inserted in the beam of the collimator as shown in Fig. 4, and can be rotated, in order to produce a polarized source with any polarization direction. Assuming that polarization cross talk of the PILOT instrument is negligible, the polarizer was shown to provide a source polarization fraction higher than 73% in the PILOT 240 μm band. The wire direction of each frame constituting the polarizer was measured with theodolites and laser-tracker. The median wire direction was measured with respect to the polarizer mechanical structure with an accuracy of about 2.4 arcminutes. A series of optical reference balls associated with the polarizer structure allow us to measure its orientation with an accuracy of 1.4 arcminutes. Globally, the direction of linear polarization is known to an accuracy of about 2.4 arcminutes, with respect to the instrument.

Optical calculations show that the direction of an incident linear polarization can be slightly rotated through the optics, as it propagates from the primary mirror to the detector [10], [11]. This rotation angle varies across the focal plane, and, according to calculations, can reach a few degrees. This rotation must be measured precisely and taken into account during astronomical data processing. To characterize this rotation, the whole focal plane has been scanned with the polarizer set at different polarization directions, in order to measure the polarization distortion. For each position, the direction of the polarizer has been measured as described above. We used the polarizer at angles 45.19±0.30° and -44.81±0.30° and moved the polarized collimator point source over 25 (5×5) pixels of each array. At each position, we rotated the HWP over its full angular range (8 positions). The data is averaged for each PSF position and the PSF flux as a function of HWP position in order to derive polarization parameters. Fig. 10. shows the distribution of the polarization angles over the focal plane. It can be seen that the polarization direction is recovered with the right angle. The actual average recovered values are 45.19° and -44.81°. We noticed the presence of a systematic rotation across the focal plane with an amplitude of about 3°, which is distributed mostly along the cross elevation axis, as expected from the symmetry of the optical system.

Figure 10.

Map of the recovered polarization angles for point sources displaced over 5×5 pixels of each array on the PILOT focal plane. The two left panels show the recovered orientation for the Transmission and Reflexion arrays for an incident polarization angle of 45.19°. The two right panels show the recovered orientation for the Transmission and Reflexion arrays for an incident polarization angle of -44.81°.