Spatial frequency in text: an informal approach

Dear LVTF,
Forgive typos and grammatical errors.

Spatial frequency is one way to analyse contrast sensitivity.  It is based
on one simple fact. Every image can be realizes as an sum of sine waves.
There are a lot of variables: the frequency, the angle they come from - the
phase, and many others.  These facts lead to the image Andrew sent out.
Frequency really influences the visibility of waves and the contrast
required to see small frequencies.

Avoiding the formal proof, let’s look at text.  While a picture of a dog
doesn’t give much faith to the notion that every image is made up of sine
waves, a page of text looks like it does have wavelengths.  Each font has
its own spatial relationship with foreground and background, and it is
quite rhythmic. Moreover, letter groups are broken into words and words are
grouped into lines, sentences and paragraphs.  It is easy to believe that
each written page has several wavelengths associated with it. The formal
proof is difficult but the intuition of this fact makes gut sense. It is
true.

Now what happens when you change spacing? All of these wavelengths change.
When you increase letter spacing, the print looks lighter. When you
increase line spacing the entire page looks lighter.  This is because there
is less dark than light, but also because the wavelength changes. If you do
all of the Spacing Criterion changes your page is a lot lighter and some
really odd effects occur.  Letters look thinner, like they have lighter
strokes. Most of these changes are be related to the spatial frequency.
That is why it is good to start with a dark font if you want a lot of
spacing. I keep my spacing as close to the source font as possible to avoid
thinning and the page looking brighter.

Best, Wayne