Limitations

Before obtaining the best resolution from a lens, designers must overcome obstacles presented by the camera. Two obstacles are the number of pixels on a camera's image sensor and the sensor's width — both of which affect image-space resolution. This is better explained in the equation,

R_img = N_p/2W_sensor

For our example, a 15.2 mm × 15.2-mm sensor consists of 2,048 × 2,048 pixels, resulting in an image-space resolution of 67.4 lp/mm horizontally. With a lens magnification of 1.52X, the object-space resolution is 102.3 lp/mm, or a minimum feature size of 9.78 µm — in line with the required 10 µm object resolution.

Another example of resolution being limited by a camera and not the lens is a diffraction-limited system where an infinity-corrected objective lens and tube lens connect to a CCD camera. The image-space f-number affects the diffraction-limited spot diameter, given by:

δ = 1.22λ/NA = (2.44λ)(ƒ/#)

where δ is the diameter of a diffraction-limited spot

λ is the wavelength of light used to image the scene

NA is the lens' numerical aperture

ƒ/# is the f-number

If λ is 0.55 µm and ƒ/# is 10, then the resulting spot diameter is 13.42 µm. For a pixel size greater than this value, the system resolution is camera-limited. But when the pixel size is smaller, as in our example, system resolution is limited by the lens, in which case choosing a camera with a smaller pixel size does not affect object resolution.

To reach the 10 µm resolution goal requires a larger lens to lower ƒ/#. Solving the diffraction-limited spot equation for ƒ/# and inserting the desired value for δ gives ƒ/# = 7.45. Therefore, any lens large enough to lower ƒ/# to less than 7.45 is appropriate resolution for the assembly robot machine vision system.

These equations for a diffraction-limited vision system apply to two-lens, as well as multi-element lens systems. Even with aberrations, these equations are useful for quickly evaluating whether or not a vision system meets specific requirements.

For more information, contact Edmund Optics at (800) 363-1992, visit edmundoptics.com, or write the editor atctelling@penton.com