Freeform Optics Metrology

In order to guide and evaluate computer controlled fabrication processes, good surface metrology data is essential. Simply, you cannot fabricate optics if you cannot measure them. Most common and the standard methodology for freefrom optics is an interferometric test utilizing a null configuration. Especially a computer-generated holograms called CGH is often used in order to create a laser beam wavefront matching the target freeform surface shape.

In the GMT primary mirror testing tower, a coherent HeNe laser beam from on interferometer goes through folding spheres and a CGH. The beam will propagate about 23 meters down, and the flat of the freeform GMT mirror surface. If the wavefront shaped by the CGH matches the mirror shape on the test, the laser beam will retro reflect to make an exact round trip all the way back to the interferometer. This is called a null configuration. Then the interferogram will measure the mirror surface shape down to nanometers of accuracy by sensing the small deviation from the null fringe pattern.

The interferometric test will work. Excellent If the shape of mirror is near ideal or near completion. However, during the initial phase of fabrication, the surface of the mirror is far from the ideal design yet. So as you see on the right side, many parts of the mirror does not even send back the beam as DCGH intended.

But the light reflects off to an uncaptured directions, since the surface cannot be measured, the computer-controlled tool time fabrication cannot be simulated and guided. Thus, a high dynamic range metrology solution on the left side is necessary. The SCOTS technology is a high precision deflectometry measurement system.

As you can see, it measures all the large error areas with its higher dynamic range. This video explains the concept of deflectometry measuring a freeform chicken. The video records the blinking facets of the chicken patty. There are known light bulb sources. We also knows the location of the chicken. Finally, the camera aperture location is also known.

At any blinking moment, a ray from the light source reflects off the facade of the chicken body and gets into the camera aperture. A simple law of reflection with a geometrical ray trace, you can data mine the local surface slope of the facet. By recording the video, until all facets blink once, you can determine the local slope of each facet. A deflectometry is a direct slope measurement. The concept can be realized using modern electronics.

The light source is now replaced with a pixelized display, such as an LCD monitor with millions of pixels, or you may call them millions of precisely located light bulbs. The chicken is now replaced with a unit and a test at a known location. Camera is looking at the unit and the test to capture the signal from the reflections. The pixels on display may be turned on and off one by one or displayed sinusoidal phase-shifting fringes, or encode multiplex patterns to increase the measurement accuracy and speed.

They are measured surface slope distribution are integrated in order to produce the surface height distribution both deflectometry and interferometry show an excellent match in measuring a 6.5-meter astronomical mirror. Comparing two independent metrology data is critical and important in large optics manufacturing because it crosschecks and confirms each other’s measurements.

The LBT adaptive secondary mirror, which changes its membrane mirror shape, was tested using that deflectometry solution also. Due to the high dynamic range, the test can measure various deformation modes of the adaptive optics. The measured trefoil deformation of about 1 micron RMS magnitude is shown on the right side.

One other very important modality of freeform metrology is a dynamic measurement. A traditional deflectometry using a grayscale phase-shifting pattern requires at least six phase-shifted measurements to acquire sufficient data solving six unknowns in the set of fundamental equations.

There are three unknowns in x and other three in y sloppy calculations if the data petition to measure all the surface local slopes can be made in a single shot. A moving object can be continuously measured by applying a multiplex pattern using red, green, and blue pixels, along with both x and y spatial frequency domain, or six measurements can be accomplished from a single shot image acquisition.

Each frame in a movie shown at the top actually includes all six information to calculate the instant surface shape at a moment. Three in each color channel can be separated. Then Fourier domain filtering is applied to separate the x and y spatial frequency components. Finally, all six images at the bottom are successfully decomposed from these single multiplex image at the very top.

This setup shows the concept implementation utilizing a commercial mobile phone providing a display and camera in the single unit. The unit on the test was a precision deformable mirror. The multiplex pattern was displayed on the phone display. The deformable mirror was continuously driven into a Trefoil shape change using actuators. The video was recorded using the mobile phone camera and processed to calculate the dynamic surface shape change.

The processed data shows the dynamic motion of the deformable mirror on the test. It successfully covers the entire 7-micron peak-to-valley surface shape deformation range. This enables a dynamic metrology of precision, freeform optics. This can be especially useful for large optics manufacturing application. Because various environmental variations and vibrations may cause a large optics continuously varies during a measurement. Revolution in metrology advances the freeform optics manufacturing process.