THIN LENSES – SHIFT & TILT PHENOMENA

Engineering Fundamentals

INTRODUCTION

Mounting thin lenses to their mechanical interfaces comprises imperfections to the initially designed optical paths due to manufacturing and assembly tolerances.

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Quantification

This sheet provides qualitative information about the phenomena because derivation of the shifts and tilts of the image as a result of the lens and/or object movement is extensive and non-transparent. Therefore a Matlab® code is provided with the necessary computations for lens x, y, \theta and object \theta, such that they can be combined at will.

Initial conditions
Lenses - Shift and tilt phenomena - Initial conditions

f
n
r_1, r_2
o, i

= focal length (average)
= refractive index of lens (medium air/vacuum: n_m=1)
= incoming radius, outgoing radius
= object distance, image distance

Focus distance f, object o and image i distance: \frac {1}{f} = \frac {1}{i} + \frac {1}{o}
Magnification: m=\frac {i}{o}

Lens x = object -x
Lenses - Shift and tilt phenomena - Lens x = object -x
Lens y = object -y
Lenses - Shift and tilt phenomena - Lens y = object -y
Lens tilt
Lenses - Shift and tilt phenomena - Lens Tilt
Object tilt
Lenses - Shift and tilt phenomena - Object Tilt
Lens y + lens tilt
Lenses - Shift and tilt phenomena - Lens y + lens tilt
Lens x, lens, y, lens tilt, object tilt
Lenses - Shift and tilt phenomena - Lens x, lens, y, lens tilt, object tilt
Lens radii

Due to manufacturing also the incoming and outgoing radii of the lens can differ. Consequently the focus distance is affected:
\frac {1}{f}=(n-1)\ \left(\frac {1}{r_1}-\frac {1}{r_2}\right)

This page uses QuickLaTeX to display formulas.