Frequency Doubling

from “Visual Phenomena & Optical Illusions”

Warning: this phenomenon requires much goodwill on your side…

What to do & observe

Short version. How many black stripes do you see on the right? Probably four. Now press ‘slow’. How many are there now? – I did not change the number of stripes, just the speed with which they shift.

Longer version. The grating on the right comes up set to a low spatial frequency, rapidly phase inverting (=high temporal frequency). To my chagrin the phase reversal has many hiccups, it stammers (explanation here). Pick times where phase reversal is regular and ask yourself “how many vertical black stripes do I see?”. You will probably see four. Now switch to a low temporal frequency (press ‘slow’) and observe that there are actually only two vertical black stripes. That’s frequency doubling – you see twice as many stripes as there are if the following conditions are met (1) temporal frequency is high, (2) spatial frequency is very low and (3) contrast is high.

Choose a high spatial frequency (press ‘hi’) and then switch the temporal frequencies between slow and fast – clearly no frequency doubling occurs for such narrow-striped (=high spatial frequency) gratings.

Comment

The phenomenon was reported by Kelly 1981. The figure on the right depicts visual sensitivity vs. temporal and spatial frequency (combining the de Lange curve with the contrast sensitivity function CSF). The striped gray area roughly outlines the range where frequency doubling occurs.

For explanation, “only a bit of non-linearity” is required.

The frequency doubling phenomenon has made it into a clinical test –not a bad career– with the following quirks:

1. There was a time (after Quigley 1987) where one thought that in early glaucoma the magnocellular system is preferentially affected.
2. Ted Maddess looked a frequency doubling using both ERG/PERG and psychophysics and suggested it be a test of the M_y subsystem [the cat X/Y-systems do not map on to the Parvo(Pβ) / Magno (Pα) systems; rather cats don’t have the Parvo (≈colour) system, and their x/y map into the primates’ M_x/M_y].
3. From this the spatially resolving Frequency Doubling Test (FDT) was developed (e.g. Demirel et al. 1999), now commercially available (Humphrey tests at 0.25 cpd and 25 Hz).
4. The FDT tests the contrast threshold where flicker is just perceived. Ironically, at low contrast no frequency doubling occurs!
5. It is the current consensus that the magnocellular system is not preferentially affected in early glaucoma (Johnson 2000, Crawford et al. 2000, Yücel et al. 2001, 2003).
6. Still the FDT performs, to a degree, as does any flicker test in glaucoma…

Sources

Kelly DH (1981) Nonlinear visual responses to flickering sinusoidal gratings. J Opt Soc Am 71:1051-5

Quigley HA, Sanchez RM, Dunkelberger R, L. LHN, Baginski TA (1987) Chronic glaucoma selectively damages large optic nerve fibers. Invest Ophthalmol Vis Sci 28:913–920

Maddess T, Goldberg I, Dobinson J, Wine S, Welsh AH, James AC (1999) Testing for glaucoma with the spatial frequency doubling illusion. 39:4258–4273

Zeppieri & Johnson “Frequency Doubling Technology (FDT) Perimetry” (at the International Perimetric Socienty)

Crawford ML, Harwerth RS, Smith EL 3rd, Shen F, Carter-Dawson L (2000) Glaucoma in primates: cytochrome oxidase reactivity in parvo- and magnocellular pathways. Invest Ophthalmol Vis Sci 41:1791-1802

Yücel YH, Zhang Q, Weinreb RN, Kaufman PL, Gupta N (2001) Atrophy of relay neurons in magno- and parvocellular layers in the lateral geniculate nucleus in experimental glaucoma. Invest Ophthalmol Vis Sci 42:3216–3222

Ansari EA, Morgan JE, Snowden RJ (2002) Glaucoma: squaring the psychophysics and neurobiology. Brit J Ophthal 86:823–826

Yücel YH, Zhang Q, Weinreb RN, Kaufman PL, Gupta N (2003) Effects of retinal ganglion cell loss on magno-, parvo-, koniocellular pathways in the lateral geniculate nucleus and visual cortex in glaucoma. Prog Retin Eye Res 22:465–481