4 Calibration of NAOS and CONICA static aberrations

  
4.1 Introduction

An appropriate way to describe the shape of a wavefront in the telecope pupil is by using Zernike polynomials (Noll 1976). A set of Zernike coefficients indicates the linear combination describing the present wavefront. As a matter of course, we can regard this set of coefficients as a vector. We refer to the Noll notation (Noll 1976) which labels the focus with 4, the tangential and sagittal astigmatism with 5 and 6, coma with 7 and 8, and so on. Since the coefficients for piston (1), and tip-tilt (2, 3) are extraneous to the image quality they are dropped.

An extensive examination of the variety of error sources due to the practical and instrumental constraints was done in the preceding Paper I. The induced aberrations due to defocusing by a shifted object in the CONICA stand-alone case have been simulated and proven to be negligible. The influence of the pupil shape and its numerization have been evaluated, errors taken in account with regard to the camera pixel scale and the defocus distance deviations have been simulated and the problem of different object structure was considered. Furthermore we focused in detail on the handling of data reduction, e.g. the influence of the different noise sources such as readout noise or pickup noise. In Paper I we state that all these error sources accumulate to $\pm 35$ nm rms for the focus coefficient (4). Since the presented calibration data of this paper are acquired with an optimized Zernike tool, the expected error should be well below this number. The accuracy of the higher order coefficients has not changed and amounts to about $\pm 5$ nm rms.

In this section we describe how the overall wavefront error can be decomposed and assigned to its corresponding optical components. Then we present the experimental results for one camera objective and some selected filters of CONICA as well as the results for the dichroics of NAOS.

  
4.2 Disentanglement

In the preceding sections we described how the static non-common-path wavefront error can be measured, whether for CONICA stand-alone or for the entire instrument NAOS-CONICA. However, each determination of the wavefront error is only valid for the particular instrument configuration in which it was measured. The tremendous number of instrument configurations makes it impractical to perform these calibrations for any possible instrument setup. For a practical application we need to split up the measured wavefront aberrations and assign the corresponding contributions to the divers optical components. This allows the construction of a configuration table with entries for each optical component of the instrument. When a special instrument configuration is selected, the corresponding wavefront error contributions can be read out, added together and delivered to the AO system. This enables the DM to pre-correct for the current static wavefront aberrations.

In principal, we have to differentiate between three categories of optical components in the imaging path: the NAOS dichroics, the CONICA filters and the camera objectives.

The contribution of the NAOS dichroics $a^{{\rm dichro}}_i$ can be determined by subtracting the overall NAOS-CONICA instrument aberrations $a^{{\rm NCtot}}_i$ from the total CONICA instrument aberrations $a^{{\rm Ctot}}_i$:

$$a^{{\rm dichro}}_i = a^{{\rm NCtot}}_i - a^{{\rm Ctot}}_i.$$ (2)

The vector components are labeled by the Zernike number i running in our case from 4 to 15. Regarding the PD estimations of the different CONICA filters for one camera objective (see Fig. 4 and Sect. 4.3) we ascertain that generally the filter aberrations $a^{{\rm fil}}_i$ are small and mainly the achromatic camera objective aberrations are seen. In any case the filter aberrations are not correlated with each other nor with the camera ones. This suggests that we can deduce the camera objective contribution by applying the median to the total CONICA internal aberrations $a^{{\rm Ctot,fil}i}_i$. We prefer the median instead of the mean to avoid taking into account highly aberrant filters. The filter i which was used to determine the corresponding total CONICA internal aberration $a^{{\rm Ctot}}_i$ is indicated by ${\rm fil}i$. The camera objective and the residual filter contributions are obtained by these relations:

$$a^{{\rm cam}}_i = \mbox{median}(a^{{\rm Ctot,fil}1}_i, a^{{\rm Ctot,fil}2}_i, ..., a^{{\rm Ctot,fil}n}_i)$$ (3)

$$a^{{\rm fil}}_i = a^{{\rm Ctot}}_i - a^{{\rm cam}}_i.$$ (4)

The separation of the wavefront aberration into the contributions associated with the three categories of optical components (NAOS dichroics, CONICA filters and camera objectives) is only possible when we make use of both ways to introduce a focus shift, i.e. the DM to determine the NAOS-CONICA overall aberrations and the Zernike tool to determine the total CONICA aberrations. In addition, we note that even if we refer to these three categories by the notation dichroics, filters and objectives, the other components in the optical path are included, as well, even when they are not mentioned explicitly. E.g., the aberrations of the CONICA entrance window are included in the dichro aberrations and the aberrations of the CONICA collimator are an inextricable part of the camera aberrations.

  
4.3 Calibration of CONICA: Camera and filters

Figure 4: CONICA internal aberrations measured by 8 NB filters in J- and H-band with camera objective C50S and pinhole pair 0/2 mm. The thick line indicates the median representing the camera aberrations.

Figure 5: CONICA internal aberrations measured by 19 NB filters in K-band with camera objective C50S and pinhole pair 0/4 mm. The thick line indicates the median representing the camera aberrations. The dashed line highlights the aberrant filter NB2.09 which is picked out for the demonstration images in Fig. 6.

Figure 4 shows the aberrations for all eight narrow band filters in J- and H-band of CONICA. The camera objective C50S and the pinhole pair (0/2 mm) is used to obtain the calibration data. The fourth coefficient $a^{{\rm Ctot,fil}i}_4$ expressing the defocus shows a peak-to-peak variation of up to 60 nm. This implies a slight imprecision of coplanarity of the filters in the cold environment. The other measured coefficients associated with the different filters noticeably resemble each other. This is evidence that these narrow-band filters contribute little to the total aberration of the system and mainly the camera objective aberration is seen.

Figure 5 displays the calibration results in the K-band. In total, 19 filters have been calibrated using the pinhole pair 0/4 mm. One of the strongly aberrant filters (NB2.09) is highlighted by a dashed line. A large defocus in comparison to the other ones is detected. This filter is expected to have a striking error of coplanarity. It is not surprising that the strong defocus comes along with a particularly high spherical aberration (i=11). The other highly aberrant filters show the same behaviour in comparison with the common filters of minor aberrations. The spherical aberration expresses the next order of a radial symmetric Zernike mode. The probability that a strong default of coplanarity induces only a defocus and does not concern higher orders is small. The PD input images of this aberrant filter is depicted at the bottom of Fig. 6. The right image shows the PSF registered in focus, and the left image a PSF having introduced a defocus of 4 mm. Already the in-focus image reveals a strong degradation, but especially the phase inversion due to the high defocus can be clearly seen in the out of focus image. A bright spot emerges in the center of the "donut''. On the top of this couple of images another couple of images is depicted. These are the PD input data of a filter (NB2.06) with normal behaviour and without strong aberrations.

As described in Sect. 4.2 the median of each Zernike number of the whole set of vectors yield the vector describing the camera contribution.

Figure 6: Comparison of PD input images of a filter with small aberrations (NB2.06, on the top) and a filter with high aberrations (NB2.09 at the bottom). The in-focus images are placed on the left side, the out of focus images on the right side. The defocus distance is 4 mm for both filters (f/15).

The accuracy of separating the camera aberrations from the raw aberrations (filters including camera) by the method described above is striking. The median aberrations for the filters of the two different wavelength regions plotted in Figs. 4 and 5 are compiled in Table 2. The deviations of both median values are clearly below the expected error (see Sect. 4.1). Table 2 lists these median coefficients taken from all NB filters in J-, H- and K-band. Keeping in mind that the achievable precision is a few nm we state that the camera aberrations are very small. The highest contributions arise from the focus term (4) and the astigmatism (5, 6). Section 5.3 gives an idea of the impact on the image quality dealing with Zernike mode aberrations in this order of magnitude. The residual filter aberrations are obtained by Eq. (4). In general, besides the focus coefficient and a few deviating filters these values are close to zero, too.

   

Table 2: Camera aberrations in nm RMS by the median over the filter + camera aberrations in the bands J, H (pinholes 0/2 mm), K (pinholes 0/4 mm) and all bands (J, H, K).

Bands for median	4	5	6	7	8	9	10	11	12	13	14	15
J, H	-12	-34	30	-6	4	2	13	-8	2	0	9	-1
K	-15	-39	27	-10	7	3	15	-9	2	0	6	-1
J, H, K	-15	-39	27	-9	6	2	13	-9	2	0	7	-1

4.4 Calibration of NAOS: Dichroics

The calibration data are obtained with the fiber at the entrance focal plane of NAOS using the adaptive optic system itself for defocusing (see Sect. 3.2). Since the Zernike coefficients for the NAOS dichros are determined differentially, i.e. by subtraction of the total CONICA aberrations from the NAOS-CONICA overall aberrations, we can choose any reference camera and filter to perform the measurements as long as the components stay the same. A good choice is camera objective C50S and filter FeII1257. This objective oversamples even in the J-band and the filter has a small wavelength and therefore yields a higher accuracy in sensing wavefront errors. A suitable distance for the focus shift at this filter wavelength in the f/15-beam is 2 mm. We can calculate suitable defocus distances using Eq. (1).

In the following the properties of the five NAOS dichroics are itemized:

• VIS: Visible light to WFS; J, H, K, L and M to CONICA;
• N20C80: 20% of the incoming light to WFS; 80% to CONICA (J, H, K);
• N90C80: 90% of the incoming light to WFS; 10% to CONICA (J, H, K);
• K: K to NAOS; J and H to CONICA;
• JHK: J, H an K to NAOS; L and M to CONICA.

Four of these five dichroics have been calibrated. The dichroic JHK is omitted since only light in L and M band reaches CONICA. It is unreliable to sense the small wavefront errors of NAOS-CONICA at these wavelengths. Furthermore there is no need to, because the small static aberrations become completely negligible in L and M.

The calibration results are compiled in Table 3 and Table 4. The first table lists the direct PD results. Any correction performed by these coefficients would only apply to the instrument configuration that was used to obtain the calibration data. The second table lists the aberrations directly assigned to the dichroics. These were obtained by subtracting the total CONICA aberrations that have been measured with the same filter and camera objective using the Zernike tool. It is noteworthy that the sensed astigmatism (Zernike number 5, 6) in the separated case is higher than in the overall case. Obviously a part of the camera astigmatism is compensated by the dichroics.

It is noteworthy that this tendency applies for all dichroics. Different reasons can cause this behaviour. First, the inclination of the dichroics artificially introduce an astigmatism. Even if the NAOS dichroics are designed for prism shape and do correct for this effect, a residual error cannot be excluded. Furthermore a certain amount of astigmatism can be introduced by components other than the dichroics lying in the same part of the light path, e.g. the output folding mirror or the CONICA entrance window (see Fig. 1). Nevertheless, it is not a limitation of the calibration method but only a question of assigning the contribution of the wavefront errors to the different optical components. In the end, only the sum of all aberrations has to be correct.

   

Table 3: NAOS dichros, overall NAOS-CONICA aberrations in nm rms, reference filter: FeII1257.

Dichro	4	5	6	7	8	9	10	11	12	13	14	15
VIS	15	-5	24	-6	23	5	-8	-9	7	-13	-7	3
N20C80	2	-1	42	-2	30	5	-4	14	-1	-19	-8	4
N90C10	-7	-3	36	-3	19	6	-5	-28	1	-9	-9	1
K	-8	14	-17	-4	18	3	-5	-6	7	-14	-10	2

   

Table 4: Separate NAOS dichro aberrations in nm rms.

Dichro	4	5	6	7	8	9	10	11	12	13	14	15
VIS	-18	37	-5	3	16	2	-21	-44	6	-13	-14	6
N20C80	-32	41	13	8	23	1	-17	-21	-3	-18	-15	6
N90C10	-41	38	7	7	12	3	-18	-64	-1	-9	-16	4
K	-42	56	-47	5	11	-1	-18	-42	5	-14	-17	5