Shade 10 Appendix 1 Cameras and Lenses

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Shade simulates most features and characteristics of real-world cameras. The degree of similarity between a real camera lens and the simulated lenses in Shade makes it extra helpful to understand how cameras and lenses work when adjusting camera settings in Shade.

Contents

Focal Length and Angle of View

The focal length of a lens in the real world is the distance between the point that we refer to as the rear principal plane (second principal point) and where the focal point (the photo surface) intersects the optical axis. The rear principal plane is defined as the plane at which rays entering parallel to the optical axis of the lens start converging to the focal point. (Figure 1)

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Figure 1: Lens Focal Length

When a parallel ray forming an angle of w degrees with the optical axis passes through a lens with a focal length of f and produces an image with a length l on the focal plane, then:

l = f tan w

(Figure 2 shows l as y’)

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Figure 2: Image Position and Size

When 2l is the size of the photo surface, 2 w is the angle of view. Generally, when the term “angle of view” is used to describe a lens, the diagonal length of the photo surface is 2l; this is sometimes called the diagonal angle of view. An angle of view sometimes shares the same definition as the range of the subject being photographed - that is, the angle of the field of view. (Figure 3)

The angle of view depends not only on the focal length, but also on the size of the photo surface - the focal plane. For instance, in the case of 35mm film, the photo surface is 36mm x 24mm, so that the length of the diagonal is:

(362 + 242) 1/2 = 43.3

and

2 w = 2 arctan ((43.3/2)/f)

In the case of a standard f=50mm lens:

2 w = 2 arctan ((43.3/2)/50) = 46.8 degrees

is obtained. Changes in the angle of view will affect the sense of perspective, that is, the realization of perspective and size when looking at a 2D image.

Changing the angle of view with the camera fixed will result in changes in the size and angle of the field of view of a subject. Changing the angle of view by moving the camera so that the size of the major subject remains constant will result in changes in the perspective of the major subject and background.

Shade simulates a 35mm camera as the basis for focal length. The focal length is displayed in the zoom value text box, and can be varied over a range of 9 to 720mm using the joystick. Precise values can be entered without restriction.

In Shade, the longer of the vertical and horizontal dimensions of the Image window always corresponds to the longer side of a frame of 35mm film. In other words, the angle of view of the longer side of the Image window is to be matched with the angle of view of the longer side of the film. Both ends of the shorter side in the Image window are trimmed appropriately.

The angle of view of the longer side is:

2 w = 2 arctan ((36/2)/zoom value)

whereas when the zoom value is 50mm,

2 w = 2 arctan ((36/2)/50) = 39.6

degrees (Figure 2)

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Figure 3: Angle of View

Screen Size, Angle of View and Focal Length Parameters

For example, when a photograph is synthesized, assuming 4 x 5 film for shooting and assuming that the focal length is 240mm, the angle of view of the longer side is around 27 degrees according to Table 1. If you look for a figure around 27 in the angle of view of the longer side in the “35mm” column, you will find that the focal length of the lens is around 75mm. Therefore, set the Zoom value in Shade to 75mm for rendering to match the perspective.

Table 1: Screen Size and Angle of View’s relationship to Focal Length (in degrees)

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Perspective Compensation

With Shade cameras, advanced perspective compensations including adjustment of the perspective point and screen frame, and focusing, are possible. Shade’s perspective compensation enables you to slide the lens side (referred to as the “front” in film terms) and the film side (referred to as the rear or back in film terms) upward/downward/rightward/leftward (referred to as rise and shift in film terms), or tilt forward/backward/rightward/leftward (referred to as tilt or swing in film terms), as well as to automatically compensate for tilt of vertical lines, especially when looking down at architectural structures.

Perspective and Parallel Perspective

Perspective depends on the difference in distance between each part of the subject and the Eye point. Parts which are closer to the Eye point have larger optical angles. For example, when you take a picture of a building as you look up at it (see Figure 4/Example 1 (i); the figures show Side views of how the building is photographed), upper stories appear smaller.

Note that when the lines showing the film surface are also used as the screen frame, Example (ii) shows that the photographed subject does not fit in the frame. Use parallel perspective (Examples (iii) and (iv)) to fit the photographed subject in the frame. Parallel perspective is achieved by sliding the lens and film upward/downward/rightward/leftward while keeping the optical axis of the lens and the film surface perpendicular. Example (iii) slides the lens (front) so that point 6 of the subject plane fits into the screen frame. Move the lens upward to have an effect of looking up (front rise), and move it rightward (front shift) for a horizontal subject, such as a train. In this case, the appearance of objects positioned in front and back of the subject plane will change. You will see that the ground appears different when you compare the illustrations. In Example (iv), the film surface (rear) of point 6 of the subject plane is moved to fit it in the frame. The building will move downward (back fall) and the train leftward (back shift).

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Figure 4: Perspective and Parallel Perspective

Points 1, 2, 3, 4, 5, and 6 on the subject plane are positioned at even intervals, but the intervals between points 1’, 2’, 3’, 4’, 5’, and 6’ on the film surface become gradually smaller. By aligning the surface of the building parallel to the film surface (Example (ii)), the sizes of each story will become even; points 1’, 2’, 3’, 4’, 5’, and 6’ on the film surface are positioned at even intervals.


Depth of Focus and Depth of Field

Lenses in the real world are always focused at areas around the focused surface (subject plane), and are out of focus in other areas, forming unclear (blurry) images. The focused area is perpendicular to the optical axis of the lens. The focused area exists not only on the subject plane side, but also on the focal plane side -- that is, on the film side. The focused area on the subject plane side is called the depth of field, and the focused area on the focus plane side is called the depth of focus. (Figure 5)


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Figure 5: Depth of Focus and Depth of Field

The depth of field -- that is, the contrast between the in-focus areas and the out-of-focus areas -- is used to emphasize the subject or to express solidness. Generally, the depth of field becomes large when the focal length of the lens is short, or the F number indicating aperture ratio is small, or when the subject length is long. Using the optical axis perspective will tilt the focused area. In Shade, the length of the subject plane, the amount of blur, and the tilt of the focused area can be adjusted to simulate the effects of depth of field when you use Path Tracing for rendering.

Optical Axis Perspective

Optical axis perspective is performed by tilting the sight, which is perpendicular to the optical axis of the lens and the film surface. There are three techniques: tilt the lens (front), tilt the film surface (rear), or tilt them both. Tilting the lens (front tilt, front swing) will also tilt the focused area on the subject side. (Figure 6, Examples 2 (ii), (iv))

Although tilting the film surface (back tilt, back swing) can tilt the focused area on the film surface side, it will also change the perspective of the photographed subject. Therefore, this technique is mainly used for deforming the subject. (Figure 7, Example 2 (iii))

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Figure 6: Optical axis perspective -- Front tilt, front swing

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Figure 7: Optical axis perspective -- Back tilt, back swing

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Fish-Eye Distortion

In the case of a normal lens, the angle of incidence and angle of emergence of light rays from a subject are equalized, to ensure the approximation of the subject in the image (Figure 2).

If you think about a case in which the subject is located at 90 degrees to the optical axis (angle of the field of view must be more than 180 degrees to see this subject), the height y’ of the image of the subject on the film in Figure 2 will be infinite.

Therefore it is apparent that this object cannot be photographed on a screen whose size is finite. Fisheye distortions use special projection methods, such as equidistance projection and orthogonal projection, to make the angle of emergence emitted from an object smaller than the angle of incidence, in order to capture an image (the entire field of view which fits into the angle of the field of view) whose angle of view is more than 180 degrees. The projected image is accompanied by strong barrel distortion. A type of lens generally called a diagonal fish-eye distortion projects images over the entire film surface by corresponding the photographic image with the diagonal of the photo surface from a focal length of more or less 16mm (in the case of 35mm film). A type of lens called a circular fish-eye distortion is capable of projecting circular images, and is generally used in photographing the entire sky for meteorological purposes and planetariums.

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Car images are courtesy of Hiroshi Isayama

Shade applies the rules of refraction to fit a 180-degree photographic image into a frame. When the index of refraction on the film side is n, the index of refraction on the subject side is n’ the angle of light rays entering border nn’ is q, and the angle of radiated light rays is q’ the equation:

n’/n = sin q’/sin q

will hold true, in accordance with Snell’s rule of refraction. (Figure 8)

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Figure 8: A Fish-eye Lens in Shade

When the value n’/n is greater than 1, the image will suffer from barrel distortion. When, on the other hand, the value is smaller than 1, the image will show pin-cushion distortion. The value of the fish-eye distortion in the Effects tab of Shade’s Rendering Options is the value of n’/n. Provided that q is half the angle of the view, and q’ is 90 degrees:

n’/n = 1/sin q

will be obtained. In this case, the value n’/n is always more than 1, and the image will be circular with a field of view of 180 degrees. When q is half the angle of the view of the longer side, the circular image is rendered fully along the longer side of Shade’s Image window. When q is half the angle of the view of the diagonal, the circular image is rendered along the diagonal of the Image window, whose aspect ratio is 36:24; and when q is half the angle of the view of the shorter side, the circular image is rendered fully along the shorter side of the Image window, whose aspect ratio is 36:24. Refer to Table 1 for the value 1/sinq for each focal length. For example, when the focal length is 16mm, to render a circular image in the Image window fully, set the same pixel value for the height and width of the image. Then, refer to Table 1 for the 35mm Fish-eye distortion, in the column “longer side angle of field” for the focal length of 16mm: the value is 1.338 (Example 3 (ii)). In order to render the subject fully along the diagonal of the Image window, set the aspect ratio of the Image window to 36:24, and set the fisheye distortion value to 1.2438, obtained from the “diagonal angle of field” column of the same table (Example 3 (iii)). The fish-eye distortion projection method can be used when rendering with Ray Tracing or Distribution Ray Tracing.

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Example 3: Fish-eye Distortion in Shade

Panoramas

Switching on the Panorama check box in the Effects tab of the Rendering Options will enable you to render a 360 degree view, with the Z-axis centered on the Eye point. All settings, except the position of the Eye point, are ignored, and the focal length of the camera is fixed at 15mm. The photographic image will be constant, though it will be rendered by stretching or shrinking to fit the Image window. When the focal length is 15mm, the angle of view will be around 100 degrees, based on Table 1; in this case, the most natural proportion is obtained by adjusting the width of the image to 3.6 times the height.

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This is a result rendered with the Panorama check box turned on, and the Eye point placed at the center of a road passing by a grass-covered plain.

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This result was rendered without using the Panorama function. The focal length (zoom value) was 15mm, fish-eye distortion value was 1.175, and the views were taken in four directions. |

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