How Surface Flatness Affects Optical Performance

Model 01 · Transmission

Bandpass: rays pass through

Exit-angle changes come from the effective optical-thickness profile.

Ray angles exaggerated for visibility
Power + irregularity 0.47 λ Relative surface-form error (λ P–V)
Reflected wavefront Not used in this transmit-only model
Transmitted wavefront 0.07 λ Illustrative TWD with wedge/tilt removed
Wedge beam steering 2.3 arc-sec 5″ × (1.46 − 1), transmitted path
Current path clarity 91% Visual proxy, not a guaranteed system Strehl ratio

Imaging consequence

Can the sensor still resolve it?

A Siemens star, fine line pairs, and small lettering expose blur, directional smear, and local distortion sooner than a natural photograph.

Ideal referencePerfect wavefront
Bandpass imageTWD 0.00 λ
What changed?

Power defocuses, irregularity distorts locally, and wedge moves the full transmitted image together.

How to read the target

Watch the star’s center, the thinnest line pairs, and the word FLAT. They fail first as wavefront error rises.

Power

Curvature changes focus smoothly.

Power is the best-fit spherical curvature of the nominally flat surface. In reflection, its wavefront contribution follows the doubled optical path and the AOI cosine factor.

RWD = 2 · cos(θ) · flatness

Irregularity

Local errors break the wavefront unevenly.

Irregularity is what remains after power is removed. Neighboring rays see different slopes, so fine structure smears and warps rather than moving as one coherent image.

Total form = power + irregularity

Wedge

Non-parallel faces steer the whole beam.

Wedge primarily changes beam pointing through a plate. It is normally removed as tilt when TWD is reported, so a sharp image can move on the sensor without becoming intrinsically blurry.

δ ≈ α · (n − 1)