PHASE EFFECTS

The primary goal of a tunable filter is to provide a monochromatic field over as large a detector area as possible. With the present TTF, however, the field of view is not strictly monochromatic. The effect is most acute at high orders of interference. Fig. 3(a) shows how wavelength gradients (or phase effects) are evident from a ring pattern of atmospheric OH emission lines across the TTF field. In this particular case we see rings at different wavelength appearing within the one order. The circular pattern is not centrally aligned due to tilting of the plates ( to ) to deflect ghost images from the beam.

Wavelengths are longest at the centre and get bluer the further one moves off-axis. For instruments such as TTF, the wavelength as a function of off-axis angle is
 
Here is the on-axis wavelength, equal to 2 L/m (for an air gap), where L is the physical plate spacing and m is the order of interference.

It follows from Eqn. (1) that the change in wavelength across an angle from the centre is given by
 
Since for the current Tektronix CCD, then is always . It also follows that remains fixed over a given radius, irrespective of order m. Bland & Tully (1989) derive related equations in the context of a higher order conventional etalon (sections II(c), (e)).

We define our monochromatic field by the size of the Jacquinot spot, the central region of the ring pattern. By definition, the Jacquinot spot is the region over which the wavelength changes by no more than of the etalon bandpass, . For wavelength, , the bandpass relates directly to the order m such that
 
Here, N is the effective finesse of the etalon, which in the case of TTF is approximately 40. Combining Eqns. (1) and (3) we find that the angle subtended by the Jacquinot spot is
 
For a particular etalon, the size of the Jacquinot spot depends on order m alone. Eqn. (4) shows how the spot covers increasingly larger areas on the detector as the filter is used at lower orders of interference. The absolute wavelength change across the detector remains the same, independently of order. However, its effect relative to the bandpass diminishes as m decreases.

Fig. 3(b) demonstrates how the effects of atmospheric emission can be removed during reduction. The software creates a background map by median-filtering copies of the original image, each one offset from the other by a small amount. The result is smoothed and subtracted from the original, leaving little or no night-sky residual. This technique relies on the fact that at low orders of interference, the night sky rings are lower frequency structures than the objects.

The TTF is the most straightforward application of tunable filter technology. Other, more sophisticated techniques such as acousto-optic filters exist, (see Bland-Hawthorn & Cecil 1996 for a review), although all are currently considerably more expensive. In future TTF-type instruments, phase effects will be eliminated from the outset by bowed plates. One advantage of such a design is that the TTF will no longer have to be tilted to deflect ghost reflections. Furthermore, interference coatings are notorious for bowing plates and this can be factored into the plate curvature specification. Other possible improvements are additional cavities to square up the instrument profile. All of these modifications are currently being explored.

© Copyright Astronomical Society of Australia 1997