science

Hypercentric lens

Hypercentric lens is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hypercentric lens rather than just read about it. In short: A hypercentric or pericentric lens is a lens system where the entrance pupil is located in front of the lens, in the space where an object could be located. An object that is further away from the lens produces a larger image than the same object when it is closer to the lens.

Key takeaways

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

Reference excerpt

A hypercentric or pericentric lens is a lens system where the entrance pupil is located in front of the lens, in the space where an object could be located.

An object that is further away from the lens produces a larger image than the same object when it is closer to the lens. This is in stark contrast to the behavior of the human eye or any ordinary camera (both entocentric lenses), where further-away objects always appear smaller. The lens must be larger than the object or scene being photographed (as shown).

The resulting images exhibit reverse perspective (also called inverse perspective). The geometry of a hypercentric lens can be visualized by imagining a point source of light at the center of the entrance pupil sending rays in all directions. Any point on the object will be imaged to the point on the image plane found by continuing the ray that passes through it, so the shape of the image will be the same as the shadow cast by the object from the imaginary point of light. The closer an object gets to that point (the center of the entrance pupil), the larger its image will be. This inversion of normal perspectivity can be useful for machine vision. Imagine a six-sided die sitting on a conveyor belt being imaged by a hypercentric lens system centered directly above it, whose entrance pupil is below the conveyor belt. The image of the die would show five faces (the top and four sides), because the bottom of the die appears larger than the top, whereas a normal lens would show only the top face (or, from other locations, at-most only three faces).

See also Entocentric lens Telecentric lens

References Markus Ulrich, Carsten Steger (2019). "A camera model for cameras with hypercentric lenses and some example applications". Machine Vision and Applications. 30 (6): 1013–1028. doi:10.1007/s00138-019-01032-w.

Illustrations

Worked examples

Example 1 — a first encounter with Hypercentric lens

Start with the simplest possible case. Write down what Hypercentric lens claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Hypercentric lens 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 Hypercentric lens 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 Hypercentric lens

In research: Hypercentric lens appears in science 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 Hypercentric lens 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: Hypercentric lens is common in secondary-school and first-year university syllabi. It links to neighbouring topics Machine vision, Photographic lenses, so understanding it makes those chapters shorter.
In everyday life: Look for Hypercentric lens 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.

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How to study Hypercentric lens in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hypercentric lens 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 Hypercentric lens out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hypercentric lens in simple terms?

A hypercentric or pericentric lens is a lens system where the entrance pupil is located in front of the lens, in the space where an object could be located. An object that is further away from the lens produces a larger image than the same object when it is closer to the lens.

Why does Hypercentric lens matter?

Because it connects several science 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 Hypercentric lens?

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 Hypercentric lens.