As a model of line spread of slanted edge consider the function

where

**Fig 1a**

Fig 1b | Fig 1c |

**Fig 1a** - LSF with sigma = 1 and k = 0.09; **Fig 1b** - xz section at y = 0; **Fig 1c** - yz section at x = 0;

Consider applying 2d Gaussian blur with sigma = to . Regarding the Gaussian blur's separability we can represent it as two sequenced convolutions in x and y directions:

Eq. 1

Gaussian blur has two more properties:

and

Tilde means equality up to an intensity scaling constant. The constant doesn't matter in our case because we always scale the LSF to fit in range [0..1].

Using the mentioned properties we can rewrite Eq. 1:

Thus, applying 2d Gaussian blur with sigma =
to 'ideal' slanted edge
is similar to applying 1d Gaussian blur with sigma =
to every scan
line, where *k* is the edge slope.

Oleg Kurtsev (okurtsev@quickmtf.com)