Globe effect

Key takeaways

Globe effect belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Globe effect to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Globe effect from memory before moving on to harder problems.

Reference excerpt

The globe effect, also known as rolling ball effect, is an optical illusion which can occur with optical instruments used visually, in particular binoculars or telescopes. If such an instrument is rectilinear, or free of rectilinear distortion, some observers get the impression of an image rolling on a convex surface when the instrument is panned.

Origin of the globe effect

The cause of the globe effect has been related to a non-vanishing barrel distortion generated in the process of visual perception: Already Helmholtz had constructed pincushion-distorted checkerboard patterns that he claimed to appear regular when viewed from a certain distance. More recently, systematic studies investigated the barrel distortion of human perception in test subjects and found that it is subject to a high statistical variance, i. e. varying greatly from individual to individual. The average degree of distortion is about half of the value suggested by Helmholtz, so that a large proportion of viewers are likely to perceive only an incomplete compensation of the bent edges in the Helmholtz checkerboard. The perceptual barrel distortion is sufficiently small to be unnoticeable in everyday life. However, if a rectilinear magnifying optical instrument is panned over a flat motif, the image pixels pass in front of the eye in rapid succession and the visual barrel distortion becomes visible as an apparent convex curvature of the image. This optical illusion remains hidden to the unarmed eye when turning the head, because it is prevented by the vestibulo-ocular reflex.

Formal Description

The image of an afocal optical instrument is distortion-free if the f-tan theta condition, also known as tangent condition and first defined by Bow and Sutton in 1861, is satisfied:

tan ⁡ a = m tan ⁡ A . ( 1 ) {\displaystyle \tan a=m\tan A.\qquad (1)}

Here, a {\displaystyle a} is the beam inclination with respect to the optical axis on the image side, and A {\displaystyle A} the beam inclination on the object side (or: subjective viewing angle of the image in the eyepiece and the inclination of the object with respect to the viewing direction), and m {\displaystyle m} is the magnification of the instrument. This relationship applies to all directions, so that the image is centrally symmetrical. To obtain a convenient parameterization of the degree of distortion, we introduce the general relationship

tan ⁡ ( k a ) = m tan ⁡ ( k A ) , ( 2 ) {\displaystyle \tan(ka)=m\tan(kA),\qquad (2)}

with the distortion parameter k ∈ [ 0 , 1 ] {\displaystyle k\in [0,1]} . This yields the f-tan theta condition (1) in the special case k = 1 {\displaystyle k=1} . The case k = 0.5 {\displaystyle k=0.5} is known as the circle condition and provides the pincushion-distorted pattern which was implemented by Helmholtz in his checkerboard. Yet another limit case with k → 0 {\displaystyle k\rightarrow 0} leads to the f-theta condition (also known as angle condition)

a = m A , ( 3 ) {\displaystyle a=mA,\qquad (3)}

which produces a considerably stronger pincushion distortion. The meaning of the infinite set of curves spanned by the distortion parameter is thus clear: Starting with the value 1, a reduction of k {\displaystyle k} produces an increasingly stronger pincushion distortion, which reaches its highest value at k = 0 {\displaystyle k=0} . At this point, another distortion is needed, which originates from the observer's visual perception. For this purpose, perceptual psychology introduces an abstract visual space whose properties are defined by mathematical modeling. In order to create a barrel distortion of varying strength, we define

y = l − 1 tan ⁡ ( l a ) , ( 4 ) {\displaystyle y=l^{-1}\tan(la),\qquad (4)}

… excerpt ends here. Continue reading the full article.

Illustrations

Globe effect: Fig. 2a: Animation of a regular grid after transformation with Eq. (5) and the parameter choices

k
=
1

{\displaystyle k=1}

(rectilinear imaging), magnification

m
=
10

{\displaystyle m=10}

and

l
=
0.6

{\displaystyle l=0.6}

. — Fig. 2a: Animation of a regular grid after transformation with Eq. (5) and the parameter choices k = 1 {\displaystyle k=1} (rectilinear imaging), magnification m = 10 {\displaystyle m=10} and l = 0.6 {\displaystyle l=0.6} .

Globe effect: Fig. 2b:
An instrumental pincushion distortion of

k
=
0.7

{\displaystyle k=0.7}

leads to an almost complete elimination of the globe effect. — Fig. 2b: An instrumental pincushion distortion of k = 0.7 {\displaystyle k=0.7} leads to an almost complete elimination of the globe effect.

Worked examples

Example 1 — a first encounter with Globe effect

Start with the simplest possible case. Write down what Globe effect claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Globe effect before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Globe effect ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Globe effect

In research: Globe effect appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Globe effect in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Globe effect is common in secondary-school and first-year university syllabi. It links to neighbouring topics Optical phenomena, so understanding it makes those chapters shorter.
In everyday life: Look for Globe effect outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Globe effect in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Globe effect means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Globe effect out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Globe effect in simple terms?

The globe effect, also known as rolling ball effect, is an optical illusion which can occur with optical instruments used visually, in particular binoculars or telescopes. If such an instrument is rectilinear, or free of rectilinear distortion, some observers get the impression of an image rolling…

Why does Globe effect matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Globe effect?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Globe effect.