LENSES INEL 6088 Computer Vision LENSES The function of the lens - - PowerPoint PPT Presentation

LENSES

INEL 6088 Computer Vision

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LENSES

• The function of the lens is to collect more light
• Image sensor size determines camera format
• Lens should be chosen so that all features to be measured are

covered in the image sensor, plus 10% for extra margin

• Features must be at least 3 pixels across
• If there are more than 100 features use a second camera

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• Magnification = Wcamera/WFOV
• FOV: Field of view = object area that is imaged by the lens onto

the image sensor

• WFOV=width of the FOV
• Wcamera = width of the camera sensor
• Working distance = distance from lens to object
• Thin-lens approximation: lens thickness is neglected
• Pinhole camera: no lens; images through a small hole

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PINHOLE CAMERAS

• Abstract camera model -

box with a small hole

Pinhole cameras work

in practice

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Pinhole too big - many directions are averaged, blurring the image Pinhole too small- diffraction effects blur the image Generally, pinhole cameras are dark, because a very small set of rays from a particular point hits the screen.

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THE REASON FOR LENSES

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THE THIN LENS

Focal length: distance between lens and camera plane when the object is at infinity Magnification: m = z/z’

Lens maker’s formula:

Basic Properties: (1) Any ray entering the lens parallel to the axis goes through the focus on the

• ther side; (2) any ray entering the lens from the

focus in one side emerges parallel to the axis on the

• ther side

β α β α

tan α = P z − f = P 0 f tan β = P f = P 0 z0 − f P P 0 = z − f f = f z0 − f (z − f)(z0 − f) = z2 − z0f − zf + f 2 = f 2 zz0 = z0f + zf 1 f = 1 z + 1 z0

(ignoring signs so -z ⇒ z and -y’ ⇒ y)

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SPHERICAL ABERRATION

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LENS SYSTEMS

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VIGNETTING

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OTHER (POSSIBLY ANNOYING) PHENOMENA

• Chromatic aberration

Light at different wavelengths follows different paths; hence, some wavelengths are

defocussed

Machines: coat the lens Humans: live with it

• Scattering at the lens surface

Some light entering the lens system is reflected off each surface it encounters

(Fresnel’s law gives details)

Machines: coat the lens, interior Humans: live with it (various scattering phenomena are visible in the human eye)

• Geometric phenomena (Barrel distortion, etc.)

Chromatic aberration

Light scattering (image flair)

Barrel distortion

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RESOLUTION

• Listed as resolving power in units of lines per inch/millimeter

RP=1/2d lines/mm d = spacing between pixels in the image plane This equation neglects lens distortion – usually not an issue in M.V.

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F/NUMBER

• Cone angle of the rays that form an image
• Determines
• Brightness of image
• Depth of field
• Resolution of the lens
• In MV the f/number can be taken as the ratio of the focal lens to the

diameter of the aperture; large aperture -> small f/number

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DEPTH OF FIELD

• Larger aperture ↔ more light ↔reduced depth of field
• Depth of field: range of scene (object) distances with scene points

that are in focus to an acceptable degree

• Out of focus points are imaged to circles. If the diameter of the

circle b is below the resolution of the sensor then defocusing is not significant

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DEPTH OF FOCUS D

b: maximum acceptable blur diameter d: lens’ diameter f: focal length z: scene distance (nominal plane of focus) Near plane distance Far plane distance

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EXPOSURE

E = Et

• E : amount of light collected by the camera
• E : image irradiance; intensity of light falling on the image plane
• t : duration of exposure (shutter speed)

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POLARIZATION

• Some objects have certain

features that are extremely bright, reflective or objects may be illuminated from an angle that produces intense reflection.

• Polarize filters are a solution.

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POLARIZATION

• Normally light is linearly polarized:

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POLARIZATION

• A linear polarizer filter absorb E along some directions and

transmit orthogonal to the direction of absorption.

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POLARIZER AND TRANSMISSION AXIS (TA)

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POLARIZERS

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POLARIZERS