Astronomical seeing measurements are usually made at a single wavelength and extrapolated to other wavelengths of interest using scaling laws that assume a specific energy spectrum for the atmospheric turbulence. We describe a variation of the Differential Image Motion Monitor system that provides a measure of the seeing and evaluation of the scaling law by simultaneously measuring the image motion at three different wavelengths.
©2002 Optical Society of America
Differential Image Motion Monitor (DIMM) systems have become one of the standard instruments for evaluating the seeing conditions at astronomical observing sites. These measurements are used to provide an indicator of the amount of turbulence in the atmosphere which can translate into the broadening of a point image or the wavefront irregularity due the atmosphere. It is common to present the results of these measurements in the form of the atmospheric seeing, measured in arcseconds, or as the Fried parameter (r0) [1,2]. Of the two measurements, the use of the Fried parameter has become the most common. Both the seeing and the Fried parameter are often scaled to other wavelengths by a ratio of the wavelengths raised to some power. Such scaling rules have a number of built in assumptions related to the energy spectrum of the atmosphere.
Sarazin and Roddier  have shown for the Kolmogorov energy spectrum that the image motion measured in the DIMM systems will be wavelength independent as r0 is proportional to the wavelength raised to the 6/5th power. Tartarski  showed that the wavelength dependence of atmospheric turbulence could be ignored under specific conditions; however, for measurements over large path lengths (as commonly encountered at large zenith angles) this wavelength independence may not hold. Hardy  addresses this point by describing the turbulence as being “practically independent of wavelength” but goes on to discuss the effects of atmospheric dispersion on the wavefront error (see chapter 9).
Recently, Linfield et. al.  have reported measuring the dependence of r0 as being proportional to the wavelength to the 1.43 power rather than 1.2. This implies that the image motion may retain some wavelength dependence.
In this paper we describe a variation on the standard DIMM system that allows for direct, simultaneous measurement of the image motion at 3 different wavelengths in a compact and easily adaptable configuration. The advantage of this Multiwavelength Differential Image Motion Monitor (MDIMM) system is that for the three wavelengths used both an average and an instantaneous measurement of the variance can be made which allows the frequency and duration of the turbulence to be tracked as well as an evaluation of the scaling rule for these wavelengths.
An excellent discussion of DIMM systems is provided by Sarazin and Roddier  and served as the basis for the design of this instrument. There are two standard variations on DIMM systems. Both use an aperture mask in front of the telescope to define two or more subapertures, however they differ in the approach used to keep the image formed from each subaperture separated on the imager. An optical filter can be used in both systems to provide wavelength selectivity.
Bally et al.  presented the simplest example of the DIMM technique that they called a Hartmann-DIMM (H-DIMM) which consisted of putting a Hartmann type mask at the front aperture of a telescope. This mask is little more than holes cut into a thin opaque cover. Spatial separation of the light from the subapertures on the imager for the H-DIMM is obtained by operating with the telescope slightly out of focus. An additional complication of using the defocused images is that information relayed to the imager has some of the image motion encoded as phase information, rather than as pure displacement. To account for this the measurements from the H-DIMM must be scaled to account for the defocus in order to recover the seeing.
The second approach uses an optical wedge placed over one of the subapertures at the front of the telescope. This allows the images from the two apertures to be brought to focus, but at different spatial locations on the imager. The focused spot from the subaperture with the optical wedge is moved just off axis, while the light from the other subaperture remains near the optical axis. The advantage of this approach is that it allows the images from the subapertures to be separated while avoiding the defocus error.
The DIMM systems are normally used to record the images from bright stars using a high frame rate camera. The objective is to measure the displacement of the two spots on the image frame and calculate the statistical parameters of the displacement with time. After passing through the turbulent atmosphere the corrugated wavefront, from a star or other source, can enter the telescope subapertures at different angles such that each spot moves independently. As a result the standard deviation of the mean of the spot centroid is a measure of the atmosphere’s effect on the wavefront. Since the atmospheric turbulence can change quickly, it is desirable to record the image frames at the highest rate possible. While it is desirable for the instruments to operate at rates approaching 1kHz, more typically, they operate closer to 100Hz.
3. Multiwavelength Differential Image Motion Monitor
Conversion of the H-DIMM system to multiwavelength work requires the inclusion of additional pairs of openings in the mask with appropriate filters used to select the wavelengths of interest. Similarly the wedge-based system can be adapted to multiwavelength measurements by using 5 or six wedges and 3 pairs of filters to be placed in front of the subapertures of the telescope. However, both of these systems are typically used on telescopes larger than 30cm. As a result the filters and wedges are often 50 to 100mm across or more, which can become prohibitively expensive. Also it is desirable and advantageous to measure the seeing not just on specially provided telescopes but on the largest telescopes at the site to include effects such as dome and mirror seeing .
The instrument that we describe here provides an alternative approach and eliminates the use of optical wedges and defocusing techniques for separating the images from the individual apertures. In this instrument design, reimaging optics are introduced to allow the DIMM components to be moved behind the focus of the telescope. The MDIMM system takes the light from the telescope and collimates it to a beam that then enters an optical housing similar in style to the “chamber of a revolver” that contains filters and pairs of parfocal lenses to focus each wavelength of light onto the imager. A raytrace of the system for a single wavelength through the MDIMM is shown in figure 1.
The collimating lens can be chosen appropriate to the f-ratio of the telescope such that the collimated beam over fills the optic holder. The optical holder acts both as a mask to define the light path, and a filter and lens holder. Associated with each pair of lenses are filters that select the specific wavelength. Figure 2 shows an illustration of the “revolver style” optical holder and the associated components.
Figure 3 shows a simulation of the deflection of the spots with the incident wavefront angle for the MDIMM for a particular telescope configuration. The 3 different wavelengths of light correspond to the peak wavelengths in the Johnson-Cousins filters B, V and R. The optical system was modeled in Zemax for an f/20 Classical Cassesgrain telescope with a 1.5m aperture. The light from the telescope is compressed to provide a 30mm collimated beam to the MDIMM. The 6 lenses used in the holder are 8mm diameter doublets with a focal length of 90mm. In this configuration the platescale is about 50 arcsec/mm and each point on the plot shows the displacement of the images for a change in the angle of arrival of the wavefronts at ¼ arcsecond intervals.
It is desirable to have each lens-filter pairs focused onto the same image plane to minimize the amount of image motion lost to defocus. There are two straightforward approaches available for having the three lens pairs be parfocal. The first would be to purchase one set of “off the shelf” lenses and have 2 sets of custom lenses manufactured. In the second all three lens pairs would be “off the shelf” and the chromatic shifts in the focal lengths would be offset by varying the lens positions in the holder. The later approach will be used in the first system that is developed.
Data reduction for the MDIMM system follows the same steps as for a DIMM system; except that there are two additional pairs of data to be processed. One complication in comparing the 3 data sets comes from the variation in bandwidth of the different filters and sensitivity of the camera at the various wavelengths. Careful selection of the filter spectral width with respect to the camera for specific classes of objects would simplify the normalization step that would be required before the sets could be compared. A complete description of this data reduction step will be explored and reported on in a later paper.
The MDIMM instrument provides multiwavelength measurements of the astronomical seeing and can be easily adapted to optical telescopes with a wide range of apertures. The MDIMM is an ideal instrument to test for the wavelength dependence of atmospheric turbulence, particularly over long path lengths through the atmosphere. An advantage of the MDIMM system is that by placing the optical components behind the focal plane of the telescope the optics are significantly smaller than for similar systems that place the optics at the primary telescope aperture. This characteristic makes it straightforward to adapt the MDIMM to many of the telescopes at an observatory.
1. D.L Fried, “Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1965). [CrossRef]
3. M. Sarazin and F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. , 227, 294–300 (1990).
4. V.I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
5. J.W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, New York, 1998).
6. R.P. Linfield, M.M. Colavita, and B.F. Lane, “Atmospheric Turbulence Measurements With the Palomar Testbed Interferometer,” Astrophys. J. , 554, 505–513 (2001). [CrossRef]
7. J. Bally, D. Theil, Y. Billawala, D. Potter, R. F. Loewenstein, F. Mrozek, and J. P. Lloyd, “A Hartmann Differential Image Motion Monitor (H-DIMM) for Atmospheric Turbulence Characterization,” Astron. Soc. Publ. Aus. , 13, 22–27 (1996).