The best way to determine the resolution of an optical system is to test it directly, through MTF testing. One can purchase expensive MTF testers or pay someone to do the testing, but we like cost effective methods.
Let’s start with the theory behind MTF testing. The basic idea is that the MTF of an optical system is a slice through the Fourier transform of the point spread function. Too much jargon? OK, let’s break it down. If you have not yet learned about MTF, please read our page on MTF and then come back. Next, a Fourier transform is a somewhat complicated mathematical operation. When performed by a computer, it is typically called an FFT (fast Fourier transform). Finally, the point spread function is just the image of a point source (like a star) formed by the lens. So all we have to do to measure MTF is take a high resolution picture of the image of a point source, take a cross-section of it (horizontal or vertical to make it easy) and have a computer do an FFT.
The next problem is how to do this cost effectively. Have you heard about the Raspberry Pi educational computer? You can purchase one for $35 and add a camera for another $30. Even with the SD card, wireless network adaptor and so on, your investment should be under $100. Unless you already have the parts handy, it will probably cost more for an optical rail and the parts to hold the lens, camera and point source than it does for the camera to do the job. The Raspberry Pi camera has 1.4 micron pixels, so it has enough resolution to test up to 180 cy/mm, which is plenty for most lenses. All you have to do is remove the lens from the camera (just as you would do for the resolution chart tester) and figure out how to hold the camera and Pi. We built a custom holder with an M4 thread for mounting to a post. We made a few spares, so if you are interested in pursuing this, feel free to ask if we have one left. The price is $50, including screws and standoffs. Here is a picture of our setup:
The simplest possible point source is a laser diode module. You can buy an inexpensive one with a driver circuit on ebay for less than $10. High power is undesirable and may damage the camera; 5mW is plenty. I power my laser diode with a lab power supply, but you can run the module off of batteries. One thing to verify before you buy is whether you can remove the collimating lens from the module – you’ll need to do this for a point source. If your lens needs to be tested with collimated light, you’re better off buying a high quality collimating lens from a supplier like Edmund Optical, Thorlabs or Newport. Just make sure the lens diameter is larger than the entrance pupil of the lens you’re testing. One problem with lasers is that they emit coherent light, which causes problems if you want to measure incoherent (normal) MTF. The solution to this is to limit the current to the laser diode so it is below threshold and emits spontaneous (incoherent) light rather than stimulated (coherent) light.
If you want to measure lenses with high MTF, a bare laser diode module might not be enough. They tend to be expensive, but a spatial filter will refocus the laser through a pinhole and assure you of a high quality point source. If you want to know what size pinhole to use for the spatial filter, the diameter should be
D = 2.44λF/#
where λ is the wavelength of the laser and F/# is the F/# of the beam coming out of the spatial filter.