Basic Anamorphic Operations and Concepts

1. DEFINITION OF THROW RATIO

NOTE: In the following discussion Throw Ratio (TR) is defined as:
Throw from projector lens divided by 16:9-format image width“.

It can be calculated in one of two ways (where T = Throw):

Based on 16:9-screen width (W):
TR = T/W

Based on Screen Height(H)
TR = T/(H * 0.5625)

2. VERTICAL STRETCH

An anamorphic adapter stretches the image optically by 1.33x in the horizontal direction only (1.26x for Digital Cinema applications). Therefore, to maintain geometry and match the optical expansion, the image must also be stretched vertically by 1.33x, as well.

  • In contrast to the adapter’s optical stretch, the vertical stretch is a completely digital process.
  • Digital stretch is usually a menu function of the projector. However, a few projectors do not offer vertical stretch. In this case you will need a scaler, an external device that separately stretches the image.
  • Use of scalers and individual projector menu functions are outside the scope of this article.
  • You can centrate the projector beam and focus the projector before vertically scaling the image.

Below is a graphical illustration of the vertical stretch process (your projector may use the symbols on the right to indicate the vertical stretch function):

Figure 1(a) Starting point: how 2.35:1 images are presented on Blu-Ray.
No vertical stretch. Note black “letterbox” bars above and below the image.

 

Figure 1(b) DIGITAL Vertical stretch.
All screen pixels are now used. Black “letterbox” bars have been filled with image pixels.

 

Figure 1(c) Constant Image Height: Digital vertical + OPTICAL horizontal stretch.
Geometry is restored and the image now the same height as the original 16:9 frame.

3. PINCUSHION DISTORTION

All anamorphic adapters exhibit more or less the same amount of pincushion distortion, due to the optics they employ.

Figure 2.1
Anamorphic Pincushion Distortion

Pincushion is so-called because the corners of the image extend outwards, like a pincushion.

Pincushion distortion is an inverse function of the throw ratio of the projector. Throw Ratio is calculated by dividing the throw (or projection distance) by the 16:9 (non-anamorphosed) width of the image.

The wider the beam, the shorter the throw ratio, the greater the pincushion.

You can minimize pincushion distortion on-screen by making sure the beam of your projector passes through the center of the anamorphic adapter. When the beam is thus centrated, pincushion should be even at the top and bottom of the image.

Figure 2.2
Beam centration with the XEIT-C5E

After the pincushion is equalized top and bottom of screen, a black mask can be used to further reduce the effect. Here is the same pincushion distorted image as above with a black mask around it. The pincushion becomes less obtrusive.

Figure 2.3
Masking an image with pincushion.
A rectangular mask makes the pincushion less obtrusive.

3. GRID DISTORTION
Grid Distortion is another kind of distortion common to any lens system.

In the case of anamorphic adapters it measures the deviation of the width a small horizontal section of the screen from the ideal (theoretical) width. Ideally the grid squares should all be the same size, anywhere on the screen. To derive a Grid Distortion figure we measure the width of these squares as projected at several different points of the screen to get an idea of the Grid Distortion performance of the entire optical system.

Given an average overall 1.33x expansion, Grid Distortion in anamorphic systems is always less than ideal at the center of the image, and more at the edges.

Example
Divide a 3,000mm (~120″) wide projected 1920 pixel-wide image into grid squares of 30 pixels each, resulting in a 64(Horizontal) x 32(Vertical) grid pattern.

Considering the 64 vertical grid columns only, each one of these should theoretically be 3,000/64 = 46.874mm wide.

Measuring the actual projected grid square width against the ideal grid square width (expressed as a percentage deviation) gives us our Grid Distortion figure for that position on the screen.

A projected grid square that is, say, 50mm wide thus exhibits a 100*((50/46.874)-1)% = +6.7% Geometric Distortion. Similarly, a 45mm projected grid square width exhibits -4.0% Geometric Distortion.

Point-to-point Grid Distortion metrics (e.g. “Edge-to-Center”, “Mid-to-Center”) can be compared against each other to give an indication of the overall distortion performance of the optical system, and to show how distortion varies with screen position.

Why is Grid Distortion important?

Better Geometry
Firstly, it should be obvious that too much Grid Distortion will cause the image to appear elongated horizontally at the edges of the image. Conversely it will appear compressed in the center. It is plainly desirable to reduce the extents of the distortion to as low a figure as possible.

Even Illumination
Secondly, assuming that each square on a projected image receives the same amount of light energy from the projector’s illumination system, a positively distorted grid square, being larger than it should be, will be dimmer than the ideal (same illumination, greater area). Conversely, A negatively distorted grid square will be brighter than ideal (same illumination, smaller area).

In short, the more Grid Distortion that a system exhibits, the more the final projected image will tend to being “hot” in the center and “dim” at the edges.

XEIT CM-5E Grid Distortion specifications
The CM-5E’s Grid Distortion specifications are, we believe, “the best in the business”. Extreme care has been taken with the CM-5E design, adding extra elements of glass to enable the simultaneous reduction of Grid Distortion below the standard industry figure, while maintaining sharpness and color fidelity.

NOTE: it is utterly impossible for any prism system to correct any distortion present, as prisms, by definition, use only flat surfaces. Incorporating curved (i.e. cylindrical) surfaces is the only way to reduce Grid Distortion. But even cylindrical designs have their problems. It is difficult to reduce Grid Distortion past a certain point with a simple cylindrical design. Sure, the distortion may be reduced, but sharpness and color performance suffer significantly.

This is why Xeitoptics abandoned the “simple” 2-lens design and added a third lens: to allow the simultaneous reduction of Grid Distortion, while maintaining sharpness and color performance at the highest level.

From our Specifications page, these are the CM-5E metrics:

  • Geometric/Grid Distortion:
  • Flat screen:

    @TR=1.5: Typically 7.95% edge-to-center
    @TR=2.0: Typically 4.4% edge-to-center
    @TR=2.5: Typically 2.8% edge-to-center

    The following illustration is a comparison between Xeit and Isco/Schneider measured grid distortion, showing that the Xeit distortion is appreciably lower than the Isco/Schneider distortion.

    Xeit v. Isco distortion comparison – Flat Screen only
    (see Shootout page)

    Curved Screen:
    Pincushion and geometric distortion both corrected to within <0.5% with appropriate cylindrically curved screen (curve should be calculated based on throw ratio), independent of TR.

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