# Tutorial 102: How to select a f-theta objective for your scanner ?

f-theta objective is normally used together with a galvo-based laser scanner. It has 2 main functions: focus the laser spot and flatten the image field, as shown in the image below. The output beam displacement is equal to f*θ, thus was given the name of f-theta objective. Current leading companies for f-theta objectives includes SILL optics, Jenoptik , LINOS, ULO, II-IV etc.

Left: typical scan field with curvature using single focusing lens. middle: typical result of a flat field lens. Right: flat field objective can provide flat field and f*θ at the output (Source: Thorlabs).

By asking the following questions, it is possible to narrow down the selection of the scanning objectives:

• What is the laser parameters (wavelength, average power, pulsed or CW?) -> determine the AR coating and the lens materials.
• What is the required image field size and focused spot size? -> determine required focal length.
• Is the telecentricity properties of the f-theta objective important? -> determine whether you would need a telecentric lens. For example, drilling application

So what to look at when shopping for a f-theta?

• focal length
• output beam quality
• clear aperture of the objective
• telecentric or not?
• lens materials ?
• achromatic or not?
• Would thermal shift be an issue ?

In general, a diffraction limited f-theta combined with a scanner would produce a spot size given by:

Spot size (1/e²) = (λ• f • APO • M²) / Dg, where APO is the truncation factor that depend on the ratio between aperture stop of the scanner and input beam diameter. Different ratio will give different APO value, as shown below:

 Da/Dg APO 2.0 1.27 1.5 1.41 1.25 1.56 1.0 1.83 0.9 1.99 0.75 2.32 0.5 2.44

As for other Da/Dg ratio, one can estimate the APO using hyperbolic tangential function or the formula stated in  “CVI Melles Griot All things Photonics”

Source: Jenoptik, Sill Optics & Thorlabs