Hermann Grid

German physiologist Ludimar Hermann (1838-1914) discovered this illusion while he was reading a physics text in which the figures were printed in a matrix-like arrangement. He published an article on it in 1870. Hering (1872) noted that the same illusory effect occurs in the case of a black grid with white squares (Fig. 1), hence it is occasionally referred to as the Hermann-Hering illusion. However, the illusion was first reported by David Brewster (1844), who credited it to the Reverend W.  Selwyn.

Philosophers of perception sometimes distinguish between three kinds of perceptual experience: (i) accurate (veridical) perception of the world; (ii) illusion (nonveridical perception of the world); (iii) hallucination (in which one has a perceptual experience but, nonetheless, having it does not amount to perceiving the world) (Macpherson 2013).
​ The Hermann grid is a classic example of what vision scientists call a simultaneous lightness contrast illusion, but philosophers have pointed out that it is not clear whether to best classify it as an illusion or as a kind of hallucination (Byrne 2011; Macpherson 2013). The question is whether we are inaccurately perceiving the white intersections as grey (and so undergoing an illusion), or whether we are hallucinating the appearance of non-existent grey smudges or dots. Visual illusions often involve the perception of multiple physical objects each of which can be perceived by themselves in a non-illusory fashion. For example, an individual line forming part of the Müller-Lyer illusion or an individual check in the Adelson illusion is a mind-independent object in and of itself. These objects only take on an illusory aspect as part of the complete figure - the illusion is (at least in part) a misperception of relational properties between the constituent elements, like one line appearing longer than another or one patch of colour appearing darker than another. The Hermann grid differs from these examples because the grey spots that we seem to perceive are not physical objects of the external world, but rather they are artefacts of the human visual system – and the experience of particular and private objects that do not correspond to external reality is normally classed as a hallucination. These considerations seem to support the idea that the Herman grid is a case of hallucination. Nonethelss, the Hermann grid is significantly different from a paradigm case of hallucination whereby one has an experience of seeing a pink elephant where there is no elephant (pink or otherwise) to be seen, for the hallucination in the Hermann grid is caused by perception of the grid. This difference is highlighted in Brewer’s (2011) interpretation of the Hermann grid as a case of perceiving a mind-independent object (the grid) supplemented with a systematic hallucination (the grey dots).

The classical explanation of the physiological mechanism behind the Hermann grid illusion is due to Baumgartner (1960). Baumgartner believed that the effect is due to inhibitory processes in the retinal ganglion cells, the neurons that transmit signals from the eye to the brain. To each cell there corresponds a small region of the retina called the receptive field, where photoreceptive rods and cones can trigger an electrical response in that cell. The receptive fields of adjacent ganglion cells may overlap. Kuffler (1953) used microelectrodes placed in the retinae of cats to measure the response of individual neurons subject to pinpoints of light stimulus, and showed that the receptive field can be broken down into a central disc and a surrounding annulus. Kuffler was also able to demonstrate that retinal ganglion cells come in two distinct kinds – either ON-centre or OFF-centre. It is the difference in stimulus between the centre and the surround of a given neuron that determines the strength of its response (i.e. how rapidly it fires). Baumgartner reasoned that the ON-centre ganglion cells whose receptive fields are centred on the grid crossings have 4 inhibiting bright areas in their surround, whereas those whose fields centre on ‘streets’ have only 2 inhibiting bright areas (see Fig.2). The on-centre neurons centred at grid crossings will fire less and so these locations on the grid appear darker. The disappearance of the grey patches whenever we try to focus on them is explained by the fact that the ganglion cells in the centre of the retina (the fovea) have very small receptive fields, so the range of their stimulus lies entirely inside the intersection point. Furthermore, the fact that the illusion occurs with inverted colours is neatly explained by the existence of the second kind of retinal ganglion cell, the OFF-centre neuron.
For all the attractions of Baumgartner’s account of the Hermann grid, recent decades have proven it unsatisfactory. Schiller and Tehovnik (2015) cite three main flaws: firstly, the illusion persists when we increase the size of the figure despite the fact that receptive fields are of a fixed size; secondly, the illusory effect can be greatly diminished or even removed entirely by skewing or otherwise distorting the grid in such a way that difference in stimulus between centre and surround is unchanged (see fig. 3); thirdly, the actual arrangement of retinal ganglion cells and their corresponding receptive fields is not as simple as Baumgartner supposed – midget and parasol ganglion cells exist in different ratios throughout the retina, the latter having much larger centre-surround receptive fields than the former. This complicated arrangement of excitatory centres and inhibitory surrounds, operating across various distances on the 2-D retinal image, means that Baumgartner’s localized retinal processes cannot explain the Hermann grid effect (Schiller and Carvey 2005). Modern theories of vision have tended to explain lightness contrast phenomena by appealing to cortical processes – e.g. the existence of multiple spatial filters which operate at different spatial frequencies (corresponding to receptive field size) to measure non-local contrast (Blakeslee and McCourt 2012).
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