How this calculator works
An afocal telescope increases beam diameter by the focal-length ratio and reduces paraxial divergence by the same ratio. A Galilean arrangement uses a negative input lens and has separation f2-|f1|. A Keplerian arrangement uses two positive lenses separated by f1+f2 and has an internal focus. Focal lengths entered here are positive magnitudes. Downstream diameter uses a conical envelope, rather than a full Gaussian propagation model.
Formula
M = f2/|f1| = Dout/Din = Θin/Θout. D(L) = Dout + 2L tan(Θout/2).
Worked example
Positive lenses of 20 mm and 100 mm form a 5× Keplerian expander separated by 120 mm. A 1 mm input becomes 5 mm, while 10 mrad full divergence becomes 2 mrad.
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Frequently asked questions
Which design has an internal focus?
The Keplerian design does. A Galilean arrangement avoids that internal real focus.
Does an expander increase beam power?
No. Ideal power is conserved and real optical surfaces introduce losses.
Why are focal lengths entered as magnitudes?
The design selection supplies the input-lens sign and determines the separation formula.