Vignetting manifests itself as the radially symmetric falloff in image brightness that is visible across a camera image. Typically, it is seen as a darkening of the image towards its periphery. Define radiance as the scene brightness, given by the power per unit solid angle emitted by a scene; image irradiance as the power of radiant energy falling on the camera image sensor; and image intensity as the brightness of an image pixel. The scene radiance is transformed into the image irradiance through vignetting, whilst the image irradiance is related to the image intensity by the camera radiometric response function. A complete definition of vignetting is thus the spatially dependent radiance attenuation that maps scene radiance to image irradiance. Thus vignetting consists of any reduction in radiant power between the front of the camera lens and the pixel wells of the camera sensor, i.e. by the physical make up of the camera and the lens assembly. Vignetting in images is generally parasitic and undesirable.

 

Six different causes of vignetting in digital cameras can be identified: optical vignetting, natural vignetting, mechanical vignetting, pupil vignetting, pixel vignetting and shutter vignetting. Optical vignetting describes the intensity falloff due to the blocking of optical paths by the pupils of the lens. Depending on the lens configuration, several different lens pupils may cause optical vignetting, although generally it is caused by the entrance and exit pupils. Thus complete optical vignetting is a compound of the vignetting effects of all the blocking lens pupils. Natural vignetting is the reduction in irradiance due to off-axis illumination. It is the result of three effects - inverse square falloff, Lambert's law and apparent aperture shape change. It can be shown that the irradiance falloff due to these three effects results in the well-known cos^4(theta) model, where theta is the angle between the camera principal axis and the light ray incident on the camera sensor. The influence of the remaining four vignetting types on the image intensity fall-off is generally much less significant than that of optical and natural vignetting. The extent of vignetting varies with lens settings, specifically focal length, aperture and focus.

 

Correction Solution

Rather than using specific models for the different vignetting types, many current vignetting modelling approaches tend to group the vignetting effects together and apply a general model to collectively capture the total vignetting. Typically a radial power series model is used. In contrast, we have developed a compound model that seperates optical vignetting from all other vignetting types. This new approach models the cause of, rather than the effect of, optical vignetting. Our experiments have shown that optical vignetting is not effectively modelled with a radial model as it induces a radially discontinuous intensity attenuation. Thus our compound model is designed to composite the varying effects of the different vignetting types. Model calibration is easily performed by imaging a diffused light source across a range of lens settings, thus allowing any images taken with any calibrated lens to be corrected for vignetting.

 

Key Advantages

  • Advanced mathematical model encompasses the complete range of lens focal length and aperture settings
  • Model captures natural vignette effects caused by varying entrance angle of light rays, and optical vignette effects due to lens hooding (important in long focal length lenses)

 

Examples of our calibrated vignetting correction solution applied to images from varies cameras/lenses are shown below.

Panasonic Lumix point-and-shoot: stitched panoramic mosaic before and after removal of vignetting.
Mouse over the image to see correction.

 

Nikon D200, 18-200mm lens: Original image exhibiting both natural and optical vignetting, and corrected image with vignetting removed.
Mouse over the image to see correction.

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