传感器相对照度漂移和渐晕.docx

1、传感器相对照度漂移和渐晕Sensor Relative Illumination, Roll Off and VignettingIn order to evaluate and understand issues that can be associated with vignetting (the blocking of rays that pass through the outer edges of an imaging lens), roll-off and relative illumination, sensor sizes, and formats need to be con

2、sidered. In addition to the following overview, more information on sensors and formats can be found inUnderstanding Camera Sensors for Machine Vision Applications.Figure 1:Roll-off is the decrease in relative illumination with respect to field that is not caused by vignetting, but by radiometric la

3、ws.MATCHING SENSORS WITH LENSESOne issue that often arises is the ability of an imaging lens to support certain sensor sizes. If the sensor is too large for the lens design, the resulting image may appear to fade away and degrade towards the edges; this effect is caused by vignetting. As the resolut

4、ion demands of a system increase, one of two things needs to happen: pixels need to get smaller or sensors need to get bigger. As is detailed in the sections onMTFandDiffraction Limit, continuous reduction in pixel size produces significant issues regarding the optics ability to resolve true detail.

5、 This concern, combined with the signal to noise and sensitivity issues associated with current sensor technology, results in sensors having to grow in size; such growth causes these issues regarding vignetting and roll-off, unless the proper lens is used.RELATIVE ILLUMINATIONRelative Illumination i

6、s a way of representing the combined effect of vignetting and roll-off in an imaging lens, and is generally given as a percentage of illumination at any point on the sensor normalized to the position in the field with maximum illumination. Vignetting and roll-off are two separate components of relat

7、ive illumination. An example of RI is shown in Figure 2. More details on how to read this curve can be found inLens Performance CurvesThe curve in Figure 2 shows that at its lowest aperture setting (f/1.4 the blue line), this lens has an RI of 57% of the illumination level of the image center at the

8、 corner of a 2/3 sensor. Under the same conditions, the lens has an RI of 72% in the corner of a sensor. As the sensor gets smaller, the RI improves. Also note that the RI improves as the f/# is increased; this occurs until there is no more vignetting in the lens, at which point all higher f/# setti

9、ngs will have the same illumination profile. Increasing the f/# generally does not increase the image circle size much, in that a lens designed for a particular sensor size will not perform well on a larger sensor even with the f/# stopped down.Roll-off will still occur when the lens is stopped down

10、, as that is related to the angle of the rays and not the number of rays that pass through the lens. Many lenses will have an illumination profile that is highest in the middle of the field and is either flat or declines to some lower percentage as it approaches the edge. There are rare cases where

11、the RI increases slightly across the image circle, but this is related to pupil compression and will not be covered in this text.Figure 2:A relative illumination curve showing relevant image sensor formats on the x-axisVIGNETTING WITHIN A LENSVignetting is the result of light rays not making it thro

12、ugh the entire lens system to the sensor, due to being blocked by the edges of individual lens elements or mechanical stops. This clipping of rays can be intentional or unintentional, and in some case is unavoidable. Vignetting is most often seen at or in lower f/#s, short focal length lenses, or le

13、nses where higher resolutions need to be achieved at a lower cost.Figure 3 demonstrates clipping as it may occur for the same 16mm lens at different f/#s (f/1.8 and f/4). Note the clipping of rays in Figure 3a, as indicated with red circles; these rays are not able to pass through the all of the opt

14、ics in the lens. Figure 3b, on the other hand, demonstrates an example without vignetting. The vignetting in Figure 3a could have several causes, including diameter limitations of the optics or a need to eliminate the rays to block stray light. Vignetting is sometimes purposely included in a lens de

15、sign to improve overall lens performance or reduce cost.Figure 3:A 16mm lens design at f/1.8 (a) and f/4 (b). At f/1.8 vignetting occurs where light rays are clipped by the edges of the lens.VIGNETTING TO GAIN PERFORMANCE (SELECTIVE VIGNETTING)Vignetting is often used to maximize the resolution of a

16、 lens design across the entire image circle. Since it is more difficult to direct the rays that create the edge of an image to the desired location on a sensor, higher resolution objects are generally more difficult to reproduce at the edge of the image than at the center. Rays that end up on the wr

17、ong pixel will degrade the image at that location; one way to manage this is to eliminate these rays from the system. If the undesired rays do not make it to the sensor, they cannot degrade the image. Removing these mis-directed rays, however, reduces relative illumination.Effects of Vignetting at t

18、he Pixel Level: Large PixelsFigure 4 Illustrates light rays incident on a pixel in the corner of a sensor at f/1.4 (a) and f/2 (b). In Figure 4a, some light spills onto the adjacent pixel creating image and contrast degradation. Increasing the f/# (Figure 4b) essentially creates vignetting which cli

19、ps those extraneous rays. Figure 5 illustrates this same vignetting effect at the center of the sensor. However, with these large pixels, the change in f/# has little effect on the overall image quality.Vignetting can also be purposefully designed into lenses in scenarios in which the effects from m

20、anufacturing tolerances adversely affect the control of rays, causing image degradation. The looser the tolerances on the lens, the more adverse these degrading effects can become, and tightening the tolerances is often not practical due to the increase in manufacturing cost. Often, a balance must b

21、e struck between reducing manufacturing cost and maintaining image quality. In cases where cost is a primary factor, vignetting must be utilized in an attempt maintain resolution across the field of view. Doing such will have an adverse effect on the illumination profile. Designing vignetting into a

22、 lens can be accomplished in a couple different ways: by purposefully designing the clear apertures of the individual lens elements such that they vignette severely off-axis rays, or by introducing mechanical apertures to block aberrated rays, as shown in Figure 8a.Effects of Vignetting at the Pixel

23、 Level: Small PixelsIn Figures 6 and 7, the pixels have been reduced to half the size, yielding a 4X resolution increase. In this example, vignetting by increasing f/# greatly, improves performance across the entire sensor, as opposed to the first example which only slightly improved the imaging per

24、formance in the corner of the image. All of these Figures (4 - 7) exhibit nominal design capabilities and do not account for reduced performance that results from manufacturing tolerances. With tolerances included, the need for vignetting can be even more pronounced, especially in cases where cost i

25、s a driving factor.Figure 4:Light rays incident on pixels in the corner of a sensor at f/1.4 (a) and f/2 (b). Increasing the f/# creates vignetting which clips the extraneous rays spilling onto the adjacent pixel in 4a.Figure 5:Light rays incident on pixels in the center of an image at f/1.4 (a) and

26、 f/2 (b). Increasing the f/# has no effect significant on image quality as all rays were contained in the desired pixel for each example.Figure 6:Light rays incident on pixels in the corner of a sensor at f/1.4 (a) and f/2 (b). Increasing the f/# creates vignetting which clips the extraneous rays sp

27、illing adjacent pixels.Figure 7:Light rays incident on pixels in the center of an image at f/1.4 (a) and f/2 (b). Increasing the f/# creates vignetting which prevents the extraneous rays from spilling onto nearby pixels.Demonstration of Vignetting in Different Lens DesignsFigure 8 and associated MTF

28、 curve features a standard 12mm lens design and relative illumination curve. Note the size difference of the ray bundles in 8a at the center (blue lines) and corner (green lines); the size difference demonstrates a large amount of selective vignetting. The vignetting leads to lower illumination at t

29、he edges of the image than in the center (8b). This is done in an effort to minimize the costs associated with materials and manufacturing tolerances, while maintaining reasonable performance at a lower price.The lens in Figure 9, an ultra-high resolution 12mm lens design, has a much more evenly siz

30、ed ray bundles across the field (9a) due to a low level of vignetting. This translates to much more even relative illumination across the entire sensor (9b). The lens in this example is designed using more costly materials at higher tolerances, which allows it to maintain high levels of performance

31、across the image, without the need to introduce vignetting to improve its performance. The trade off in using such a lens is that the ultra-high resolution lens is more expensive than the standard design.Figure 8:A standard 12mm lens ray path (a), relative illumination curve (b), and MTF curve (c).F

32、igure 9:A ultra-high resolution 12mm lens ray path (a), relative illumination curve (b), and MTF curve (c).ILLUMINATION ROLL-OFFIn its simplest form, the maximum brightness of a lens for some given image circle with no vignetting is limited by the fourth power of the cosine of the chief ray angle in image space. This is known as cos4q rolloff. Figure 10 shows the chief rays for the center and the corner of the image (highlighted in red).Figure 10:Imaging lens layout, highlighting the chief rays of the ray bundles belonging to the center (blue lines) and the corner (green lines)