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ACAM filter transmitted wavefront errors (TWE)

Filters used in one of ACAM's two filter wheels lie in a near-collimated beam, and the bundle of rays from each star (diameter 51 mm at wheel 1, 42 mm at wheel 2) intersects a substantial fraction of the total area of the filter. If the rms transmitted wavefront error (TWE) of the filter is >> wavelength/4, the delivered PSF on the science detector will be significantly degraded compared to the diffraction limit. It's not straightforward to predict PSF from TWE when the latter exceeds wavelength/4, but in practice we find a good approximation to be:

FWHM (arcsec) ~ TWE (waves) / 1.8

That is, filters with rms TWE > 0.9 waves will significantly degrade the best seeing at the WHT (0.5 arcsec).

In early 2011, Annemieke Janssen and Neil O'Mahony measured the TWE of most of ING's filters using a Shack-Hartmann test setup (designed by Tibor Agocs). The rms TWE (in lambda), measured over the central 40-mm area are given below for each filter (ordered by filter type and number). The quality label in the fifth column is 'OK' for TWE < 0.9, '~' for 0.9 < TWE < 1.8 and 'Bad' for TWE > 1.8.

The quoted TWE values exclude the focus term introduced by the filter (given in column 6) since it should be possible to take out most of this (but not all of it) by refocusing the telescope - see the ACAM filter focus offsets page. The quoted TWE also exclude the tip and tilt terms introduced by the filter (columns 7 and 8). (NB in ING's internal filter database the column 'TWS' records measured TWE including the focus term, i.e. bigger values than tabulated below).

An overview of the results, by filter type, is given on the ACAM imaging page. Only a few of the old Hα filters have TWE > 1.8 waves rms (i.e. are particularly bad). Stromgren V (#179) introduces an unusually large focus term.

On-sky images of stars were taken by Cecilia Fariña in August 2014, through several filters: #58 (H6559) ; #61 (H6570) ; #62 (H6553) ; #66 (H6645) ; #86 (SiII 6727) ; Sloan R . The on-sky FWHM for filters #58 and #66 (TWE rms = 3.9 and 1.1 lambda respectively) are 1.0 and 0.5 arcsec worse than ambient seeing (broadly consistent with the equation above), and the PSF for #58 is clearly distorted.

Various factors contribute to a filter's total TWE, including polishing errors and inhomogeneities in refractive index. Polishing errors usually dominate. If they leave the nominally flat surface with irregularities D rms, the TWE will be (n1 - n2) * D / wavelength, where n2 ~ 1.5 and n2 = 1 are the refractive indices of glass and air, i.e. TWE ~ 0.5 D / wavelength per surface. Multiplying by sqrt(2) for 2 surfaces, this implies a total TWE ~ 0.7 D / wavelength. If a filter has been specified to have surface flatness D < 1/4 wavelength, one expects TWE <~ 0.18 wavelengths (many of the TAURUS filters satisfy this).

Filter   No.  Diam    TWE  TWE   Defoc   Tip  Tilt
name          mm      rms  qual.
      

Broad band:                   

RGOB1      8  50*50   0.5  OK     0.6    8.8 -13.1
RGOV1     11  50*50   0.5  OK     1.1    1.2  -0.7
RGOV1     12  50*50   0.4  OK     0.6    5.4   7.4
RGOR1     14  50*50   0.1  OK     0.4   -7.5   1.2
RGOR2     15  50*50   0.4  OK     0.3    2.4   5.2
RGOI1     17  50*50   0.1  OK     0.0    0.4  -6.6
RGOZ1     20  50*50   0.1  OK     0.1    1.6   1.8
RGOZ2     21  50*50   0.1  OK    -0.1    1.4  -1.9
RGOZ3     22  50*50   0.1  OK    -0.1   -1.1  -2.7
GunnZ     24  50*50   0.2  OK    -0.8    8.1  -1.3
HarB1     25  50*50   0.3  OK    -1.1    6.0  17.8
HarB3     26  50*50   0.7  OK    -0.1   -0.4   1.9
HarB4     27  50*50   0.3  OK    -0.5   -2.4   4.0
HarB5     28  50*50   0.3  OK     0.4   -0.8  -1.0
HarV1     30  50*50   0.7  OK     0.2   15.7  11.6
HarV2     31  50*50   1.2  ~     -0.8    1.2   2.7
HarV3     32  50*50   0.0  OK     0.1   -0.7  -2.2
HarV4     33  50*50   0.0  OK     0.0   -1.1  -0.3
HarR2     37  50*50   0.5  OK     0.4   -4.6   1.3
HarR3     38  50*50   0.0  OK     0.2    1.1  -1.8
HarR4     39  50*50   0.0  OK     0.1    0.0   2.1
HarI1     41  50*50   0.1  OK    -0.7    7.9  -6.0
HarI3     43  50*50   0.0  OK     0.0    1.7   0.4
HarI4     44  50*50   0.0  OK     0.0    1.3   1.2
KPB2      47  50*50   0.7  OK    -0.2   -2.8   4.6
KPB3      48  50*50   0.9  OK    -0.2    1.2  -1.8
KPV1      49  50*50   0.5  OK     0.7    4.2  13.0
KPV2      50  50*50   0.3  OK    -0.5   16.2  -1.2
KPV3      51  50*50   0.4  OK     0.6   -2.0   0.2
KPR2      53  50*50   0.5  OK     2.3    1.8   0.7
KPI1      55  50*50   0.2  OK     0.6   -7.4   5.4
KPI2      56  50*50   0.5  OK     0.1    3.8   3.5
KPI3      57  50*50   0.5  OK     0.8    1.6  -2.8

Hα:                       

H6559     58  50*50   3.9  Bad    2.0   -1.3  13.6
H6570     61  50*50   0.5  OK     0.3   -3.5  -4.1
H6553     62  50*50   1.0  ~      1.1    8.2  -2.4
H6594     63  50*50   0.3  OK     0.3    5.2  -7.0
H6607     64  50*50   0.5  OK    -2.0   -5.2  10.8
H6626     65  50*50   0.2  OK     0.0    3.1   1.5
H6645     66  50*50   1.1  ~     -1.6    3.2  -0.3
H6695     67  50*50   0.2  OK     0.7    6.7   1.8
H6686     68  50*50   0.3  OK    -0.1   -1.0   0.3
H6695     69  50*50   2.9  Bad    1.9    6.0   1.3
H6712     71  50*50   0.3  OK    -0.1   -2.4  -5.0
H6736     72  50*50   2.5  Bad    0.4   10.4  -0.2
H6785     73  50*50   1.6  ~     -2.3    0.4  -3.5
H6834     74  50*50   1.1  ~     -0.7    3.3   0.0
H6876     75  50*50   0.9  OK     0.9    6.1   5.2
H6923     76  50*50   0.9  OK    -2.3    1.9   3.6
H7962     77  50*50   3.5  Bad    2.3   -5.9  -2.7

Misc. narrow-band:            

He4685    80  50*50   0.1  OK     0.9    5.1   0.9
H4861     81  50*50   0.3  OK     1.5    2.9  -1.3
O5009     82  50*50   0.2  OK    -0.3   -1.4   0.5
He5877    83  50*50   0.2  OK     0.6    0.6   1.9
O6298     84  50*50   0.2  OK     0.2   -0.7   0.2
N6584     85  50*50   0.2  OK     0.0   -0.1   0.3
S6727     86  50*50   0.1  OK    -0.3    2.8   1.4
O7331     87  50*50   0.0  OK     0.7    0.3   1.5
S9077     88  50*50   0.0  OK     0.0    1.1  -2.4
S9540     89  50*50   0.0  OK    -0.3    0.3  -1.0

TAURUS narrow-band:           

T4550     97  76      0.2  OK     0.4    5.0   3.0
T4570     98  63      0.1  OK     0.2    0.4  -0.4
T4770     99  63      0.1  OK     1.1    0.2  -0.1
T4868    100  63      0.4  OK     0.9    4.1  -2.0
T4880    101  76      0.1  OK     1.5    0.0  -0.1
T4883    102  63      0.4  OK     1.0   -0.1   1.4
T4898    103  63      0.4  OK     1.0    0.3   1.7
T4912    104  63      0.3  OK     1.1    0.2   1.1
T4962    105  76      0.2  OK    -0.4   -0.1   1.9
T4974    106  76      0.2  OK    -0.2    1.1  -0.8
T5000    107  63      0.1  OK    -0.1   -0.3   0.6
T5009    108  76      0.2  OK    -0.5   14.1  -1.9
T5012    110  50      0.9  OK    -0.7    8.4  -2.5
T5021    111  76      0.3  OK    -0.4   -1.2  -4.8
T5032    112  50      0.3  OK    -1.1   17.0   5.5
T5033    113  76      0.2  OK     0.0    6.8  -9.5
T5045    114  76      0.4  OK    -0.3   -4.0   3.6
T5052    115  50      0.5  OK    -0.9    2.3   0.9
T5065    116  76      0.1  OK    -0.3    0.2   1.1
T5072    117  50      0.3  OK    -0.4    1.7   7.2
T5092    118  50      0.3  OK    -0.2   22.9  -9.2
T5111    119  76      0.2  OK    -0.2   -0.8   0.2
T5129    120  76      0.1  OK    -0.2    0.8   0.5
T5145    121  76      0.1  OK    -0.1    0.8   0.8
T5162    122  76      0.1  OK    -0.2    0.8   2.0
T5175    123  76      0.1  OK     0.0    0.6   0.3
T5196    124  76      0.2  OK     0.0   -0.9   0.5
T5214    125  76      0.1  OK    -0.1    2.2  -0.1
T5232    127  76      0.1  OK    -0.1   -0.3   2.4
T5250    128  76      0.1  OK    -0.1   -0.8  -1.0
T5340    130  76      0.0  OK     0.2   -0.5  -0.2
T5700    133  63      0.1  OK     0.9   -0.8  -1.3
T5905    134  76      0.1  OK     0.7    1.1  -0.5
T5690    135  63      0.1  OK     0.7   -0.5  -0.6
T6240    136  63      0.1  OK     0.5    0.9  -0.5
T6303    137  63      0.1  OK     0.2    0.5  -0.6
T6565    139  76      0.3  OK    -0.1    5.5   0.1
T6568    140  50      0.2  OK    -0.2    7.9  -1.0
T6577    141  76      0.4  OK     0.4   17.6   2.1
T6589    142  76      0.3  OK    -0.1   -8.3  -3.4
T6589    143  76      0.7  OK    -0.1    2.2   0.0
T6590    144  76      0.0  OK     0.0    0.1   0.2
T6610    146  50      0.2  OK     0.0    5.6  -1.9
T6613    147  76      0.2  OK    -0.3    3.2   5.6
T6631    148  50      0.2  OK     0.0    0.2   2.4
T6637    149  76      0.1  OK    -0.1   -0.9  -0.7
T6652    150  50      0.4  OK     0.2    5.7  14.7
T6673    151  76      0.0  OK    -0.1    0.1  -0.8
T6673?   152  76      0.2  OK     0.1   13.9  12.5
T6685    153  76      0.1  OK    -0.1    0.8  -0.4
T6689    154  63      0.0  OK     0.0   -1.0   0.5
T6697    156  76      0.1  OK    -0.1    1.4   1.2
T6709    157  76      0.1  OK    -0.1   -0.2   1.0
T6721    158  76      0.1  OK    -0.1   -1.0   0.2
T6733    160  76      0.0  OK    -0.1    0.5   0.7
T6745    161  76      0.1  OK    -0.2   -0.1   0.4
T6757    162  76      0.0  OK    -0.2   -0.4   1.4
T6769    163  76      0.0  OK    -0.2   -0.9  -0.5
T6770    164  50      0.1  OK     0.0    0.2   1.6
T6781    165  76      0.0  OK    -0.1    0.5   1.0
T6793    166  76      0.0  OK    -0.3   -1.0  -1.4
T6805    168  76      0.1  OK    -0.2   -0.9  -1.6
T6817    169  76      0.1  OK    -0.2    0.8  -0.4
T6829    170  76      0.1  OK    -0.2    1.4   0.3
T6841    171  76      0.0  OK    -0.2   -2.1  -1.8
T6853    172  76      0.1  OK    -0.3   -0.6  -1.2
T6865    173  76      0.1  OK    -0.2    0.5   1.3
T6877    174  76      0.1  OK    -0.3    0.3  -1.3
T6889    175  76      0.1  OK    -0.3    1.2  -0.9
T4686    189  76      0.3  OK     0.5    4.8   7.1

Narrow-band:                  

O6310    176  50*50   0.1  OK     0.2    0.7  -0.6

Stromgren:                    

StromV   179  50*50   0.3  OK    -5.1    3.5   3.3
StromB   180  50*50   0.2  OK     1.2    0.5   0.1
StromY   181  50*50   0.3  OK    -0.3   -4.6  -2.2
StromHbW 182  50*50   0.2  OK     1.6   -4.7  -2.6
StromHbN 183  50*50   0.4  OK     0.7   -4.9   6.0

Sloan (new):                        

SlnU     700  60      0.2  OK     0.1    0.1   0.3
SlnG     701  60      0.0  OK     0.0    1.5   1.6
SlnR     702  60      0.2  OK     0.1    0.2   0.9
SlnI     703  60      0.2  OK     0.2    0.5   0.0
SlnZ     704  60      0.1  OK     0.0    0.3   0.2

Sloan (old):                        

SloGunR  216  50      0.1  OK     0.3   11.0   7.5
SloGunI  217  50      0.0  OK     0.4    0.2   0.8
SloGunG1 218  50      0.0  OK     0.4    1.0   1.2
SloGunG2 219  50      0.1  OK     0.4    0.7   0.4

Bessell:                      

BesB     231  50*50   0.2  OK     0.0    2.0  -0.6
BesV     232  50*50   1.7  ~      1.7   -1.0   3.3
BesR     233  50*50   0.1  OK     0.4    1.2   0.4
BesI     234  50*50   0.0  OK     0.1    0.4  -0.1

Order-sorting filters:        

GG395A   705  76      0.3  OK    -0.3    2.3   9.1
GG495A   706  76      0.0  OK     0.1    0.7   1.6

The rms errors in the Shack-Hartmann-measured TWE and defocus terms depend strongly on wavelength, and are estimated by Annemieke to be as follows:

Band          Rms error in    Rms error in
              defocus term        TWE 
                
B (3800-4900)      3.0            0.4
V (4900-5600)      0.5            0.16
R (5600-7300)      1.0            0.14
I (7300-8500)      0.7            0.03
Z (8500-9500)      0.5            0.03

The U filters have not yet been measured - the Shack-Hartmann setup used is not sensitive at these wavelengths. However, the new Sloan u filter (#700) has been used to image a focal-plane pinhole in ACAM itself, and the PSF is very good (FWHM < 2 pixels).

(Because of the variation of focus with wavelength within ACAM, it's not currently straightforward to carry out the pinhole-imaging test for filters redder than U/B.)



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Contact:  (ACAM Instrument Specialist)
Last modified: 29 April 2012