science

Modified Uniformly Redundant Array

Modified Uniformly Redundant Array 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 Modified Uniformly Redundant Array rather than just read about it. In short: A modified uniformly redundant array (MURA) is a type of mask used in coded aperture imaging. They were first proposed by Gottesman and Fenimore in 1989.

Key takeaways

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

Reference excerpt

A modified uniformly redundant array (MURA) is a type of mask used in coded aperture imaging. They were first proposed by Gottesman and Fenimore in 1989.

Mathematical Construction of MURAs MURAs can be generated in any length L that is prime and of the form

L = 4 m + 1 , m = 1 , 2 , 3 , . . . , {\displaystyle L=4m+1,\ \ m=1,2,3,...,}

the first five such values being L = 5 , 13 , 17 , 29 , 37 {\displaystyle L=5,13,17,29,37} . The binary sequence of a linear MURA is given by A = A i i = 0 L − 1 {\displaystyle A={A_{i}}_{i=0}^{L-1}} , where

A i = { 0 if i = 0 , 1 if i is a quadratic residue modulo L , i ≠ 0 , 0 otherwise {\displaystyle A_{i}={\begin{cases}0&{\mbox{if }}i=0,\\1&{\mbox{if }}i{\mbox{ is a quadratic residue modulo }}L,i\neq 0,\\0&{\mbox{otherwise}}\end{cases}}}

These linear MURA arrays can also be arranged to form hexagonal MURA arrays. One may note that if L = 4 m + 3 {\displaystyle L=4m+3} and A 0 = 1 {\displaystyle A_{0}=1} , a uniformly redundant array(URA) is a generated. As with any mask in coded aperture imaging, an inverse sequence must also be constructed. In the MURA case, this inverse G can be constructed easily given the original coding pattern A:

G i = { + 1 if i = 0 , + 1 if A i = 1 , i ≠ 0 , − 1 if A i = 0 , i ≠ 0 , {\displaystyle G_{i}={\begin{cases}+1&{\mbox{if }}i=0,\\+1&{\mbox{if }}A_{i}=1,i\neq 0,\\-1&{\mbox{if }}A_{i}=0,i\neq 0,\end{cases}}}

Rectangular MURA arrays are constructed in a slightly different manner, letting A = { A i j } i , j = 0 p − 1 {\displaystyle A=\{A_{ij}\}_{i,j=0}^{p-1}} , where

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Modified Uniformly Redundant Array

Start with the simplest possible case. Write down what Modified Uniformly Redundant Array 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 Modified Uniformly Redundant Array 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 Modified Uniformly Redundant Array 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 Modified Uniformly Redundant Array

In research: Modified Uniformly Redundant Array 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 Modified Uniformly Redundant Array 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: Modified Uniformly Redundant Array is common in secondary-school and first-year university syllabi. It links to neighbouring topics Radiation, so understanding it makes those chapters shorter.
In everyday life: Look for Modified Uniformly Redundant Array 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 Modified Uniformly Redundant Array in 20 minutes

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

Frequently asked questions

What is Modified Uniformly Redundant Array in simple terms?

A modified uniformly redundant array (MURA) is a type of mask used in coded aperture imaging. They were first proposed by Gottesman and Fenimore in 1989.

Why does Modified Uniformly Redundant Array 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 Modified Uniformly Redundant Array?

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 Modified Uniformly Redundant Array.