How to test your telescope's optics
The Hartmann Test is scientifically the best way to determine the level of optical quality in a telescope.
Photo Credit: Shawn O'Brien
Astronomers have always needed a way to test the quality of a telescope's optics. Before the twentieth century, this was done with the Star Test. This test consisted of comparing the image of a star on both sides of the prime focus. The two images are equidistant from the focal point. Specific differences in the patterns of the out-of-focus shot images easily correlate to certain aberrations, such as astigmatism. There are two main problems with this method. First, this test is greatly dependant on the observer's personal judgment. Secondly, this test is entirely qualitative, producing no numerical data with which to evaluate the extent of the different aberrations present in the system.
Around the year 1900, an astronomer named J. Hartmann developed an improved testing method, which gave the astronomy community the first truly scientific method for analyzing telescope optical quality. This process employs a mask to turn star test images into spot patterns. These inside and outside of focus spot patterns could now be compared and used to mathematically determine how much of which aberration exists at each spot on the mirror. Every spot on the inside-of-focus image has an equal but opposite spot in the outside-of-focus image. These spots can be graphically connected using a method called 'ray-tracing'. This involves tracing out the actual paths the individual light rays had to take to form an image at the specific location in each spot pattern. The best focus is determined by the minimum spot size location, where by theory every light ray should converge to a single point. Calculating the location offset for each spot and summing the offsets obtains the Hartmann Constant
When the Hartmann Test was first invented, it was only done on large, professional telescopes. It would take a team of mathematicians and physicists weeks to go through and calculate all the data from this test. Fortunately, today amateur astronomers now have computer software that can do all the tedious calculations. The Santa Barbara Instrumentation Group (SBIG) created the Hartmann Test Software that is currently commercially available. To run an analysis, all that is needed are the inside and outside of focus spot pattern images and the telescope's (f) number. The (f) number is a ratio between the focal length and the diameter of the primary mirror. The spot pattern images are obtained with a CCD camera.
Before the Hartmann test can be performed, a custom mask must be manufactured. The holes in a Hartmann mask are typically 1/15th the diameter of the primary mirror. According to the SBIG Corporation, the holes need not be precisely located, evenly spaced, round, or even cleanly cut because the analysis program they developed can compensate for these faults. The analysis software can handle up to 32 holes. Another item SBIG recommended was that the mask be made of metal, mainly for durability reasons. Typically, a second mask with five holes in the shape of a cross is made and used to perform an alignment check on the telescope's mirrors prior to performing the Hartmann Test.
Once you have constructed both of the required masks and connected the CCD to the telescope, a mirror alignment should be done first. This ensures that misalignment of the mirrors will not skew the Hartmann Test results. To perform a mirror alignment, install the mask with the cross pattern on the telescope. Set the CCD software to display the image in as close to real time (refresh rate) as possible. (Mirror alignment can also be done visually, through an eyepiece.) The focal point is where the points of the cross merge into a single object. Once the focal point has been determined, then if necessary, the mirror alignment can be adjusted to obtain the best possible focus. After all adjustments are made it is time to perform the Hartmann Test. To perform the Hartmann test, install the Hartmann test mask and start the Hartmann test software on the computer connected to the CCD. The software will require one picture to be taken outside-of-focus and another inside-of-focus. For the best results, try to get these images equidistant from the focal point. Once these images are loaded into the Hartmann program, just sit back and wait for the program to calculate your Hartmann constant. Historically, a telescope with a Hartmann constant of 0.2 or less has been considered to be of high quality. Keep in mind that it is usually beneficial to take these out of focus images several different times, due to the fact that getting them EXACTLY equidistant on either side of the focal point is very difficult. After a few runs, use the best-achieved constant as your telescope's actual Hartmann Constant.
If there is ever a question in regards to the quality of a telescope's images, whether visual or photographed, the Hartmann Test is scientifically the best way to evaluate a telescope's optics.