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What is Metrology Part 23 – Error and Perception

After a significant amount of time dedicated to this series, I have made some interesting insights. When you think of metrology and measurement, humans need to understand that we are faulty at what we do. It is difficult to have true precision in measurement. We are prone to error and degrees of various errors. Secondly, no one human has the same perception as another. This leads to various incongruities in the physical realm. We can think in terms of optics, general psychology, and a vast number of phenomena. So how do we escape faulty perception and human error? Well, that seems impossible, but I am going to venture into these topics to show how they affect measurement and metrology as a whole.

Margin of error is a statistic that shows the amount of sampling error due to random occurrences. When we have a large margin of error, there lies less confidence in the data we collect. In reference to metrology, one can think of a scanning system as our measuring apparatus. When operated by a human, various things and random occurrences can affect the margin of error within a laser scan. This can include an unsteady hand when scanning an item. One could also have a slightly unclean lens that may cause distortion within a 3D scan. The movement of a target for 3D scanning may also affect this as well. There are a slew of items that may cause a 3D scan to contain large margins of error.

Act of Perception

Perception is how we organize, identify, and interpret sensory information in order to understand or represent our environment. Perception includes the ability for us to receive signals that go through our nervous system. This results in physical or chemical stimulation of our sensory systems. This allows us to interpret and understand the information we are bombarded with on a daily basis. Examples of this include how vision occurs through light interacting with our eyes, how we are able to use odor molecules to interpret smell, as well as our general ability to detect sound through pressure waves within the air. Perception is denoted by the receiver though. This means their learning, memory, expectation, and attention are vital for how the signals are interpreted.

I bring these things up as it shines a light on a key difference between machines and humans. Machines have less working experience, expectation, and learning compared to humans. Being able to consistently distinguish a watch in 3D form is natural for most humans, but a machine can be thrown off by slight variations in form. A machine automated process may have less error in terms of pure measurement, but the interpretation of the data is still a difficult task for a machine.

Issues of Perception and Metrology

Perception is typically thought of in two forms:

Processing an input that transforms into information such as shapes within the field of object recognition.
Processing that is interloped with an individual and their own concepts or knowledge. This includes various mechanisms that influence one’s perception such as attention.

Through laser scanning, an individual is able to collect data on a physical product. This data needs interpretation for it to have tangible value. A computer device is not readily able to do so. So metrology is a field based on our innate error and psychology as humans. But that does not mean the field is useless, as we humans have an innate desire to make things quantifiable.

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What is Metrology Part 19 – Moire Effect in 3D Printing

Moire Effect

Errors are abundant when measuring objects, and we have continually come across this within our series of articles. Image processing in 2 dimensions is vital for transforming images into a 3D structure. This includes extruding a 2D image into 3D as well as stitching 2D images to create a 3D image. Today we will learn about an effect in photography that many of us notice, but are not aware of its terminology. We will also look into how this affects metrology and, subsequently, 3D printing.

The Moire Effect refers to a pattern that is created in images occasionally. A moire pattern is a large in magnitude interference pattern. This can be produced with an opaque pattern that has transparent gaps overlaid within it. To see a large display of the moire interference pattern, two patterns cannot be identical in nature. The patterns have to be rotated or have a slightly different pitch. Overall it is a pretty trippy visual and it messes with our typical human perception in a variety of ways.

Moire Effect 3D Printing

Constructing 3D images from 2D images is a difficult problem. An object that is 3D scanned is vulnerable to the moire effect. When doing a 3D print, the moire effect arises when you notice zebra like stripes on the surface of a print. To stop this it is critical to have great image processing on the 2D level. It seems as though it is nearly impossible to make a roughly perfect 3D image because of the impossibility of creating a perfect 2D image. This is okay, but we are still trying to attain the highest precision possible.

There is a lot of interesting math behind this effect as well. The essence of the moiré effect is the (mainly visual) perception of a distinctly different third pattern which is caused by inexact superimposition of two similar patterns. The mathematical representation of these patterns is not trivially obtained and can seem somewhat arbitrary. In this section we shall give a mathematical example of two parallel patterns whose superimposition forms a moiré pattern, and show one way (of many possible ways) these patterns and the moiré effect can be rendered mathematically.

${displaystyle {begin{aligned}f_{1}&={frac {1+sin(k_{1}x)}{2}}\[4pt]f_{2}&={frac {1+sin(k_{2}x)}{2}}end{aligned}}}$

Moire Effect Mathematics

The visibility of these patterns is dependent on the medium or substrate in which they appear, and these may be opaque (as for example on paper) or transparent (as for example in plastic film). For purposes of discussion we shall assume the two primary patterns are each printed in greyscale ink on a white sheet, where the opacity (e.g., shade of grey) of the “printed” part is given by a value between 0 (white) and 1 (black) inclusive, with 1/2 representing neutral grey. Any value less than 0 or greater than 1 using this grey scale is essentially “unprintable”.

Moire Effect Background

When is the Moire Effect most prevalent? A terminology that is important to understand within metrology is strain measurement. Strain is a measure of the deformation of a body due to a force being applied to it. Strain is also the mathematical change in dimension of a body when a force is applied. Thus, strain measurement is focused on document the changes within dimension based on force applications. This is great when we want to measure deformations, but not for when we want to remove the possibility of them occurring through a 3D print. There are image scanners that have a descreen filter. These filters typically remove Moire-pattern artifacts. These are produced when scanning halftone images to produce digital images.

In conclusion, the Moire Effect as an interesting visual effect that occurs within the 2D realm and it readily affects the 3D world. With metrology technology, it is one of the various phenomena that can interfere with a high precision scan of an object.

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What is Metrology Part 13: Object Recognition

3D Perception

We as humans have faulty perception of the physical environment we live in. Although we are able to distinguish 2D items and 3D items, we do not have the ability to measure them in real time with numeric values. We need to use outside devices to assist us. We have discussed at length these topics within our metrology series, but today we will take a look specifically at a subsection of knowledge within this field and computer vision. With computer oriented object recognition, humans are attempting to make the world more precise through the lens of a computer. There are a variety of things that get in the way of precise object recognition.

Object recognition is defined as technology in the field of computer vision for finding and identifying objects in an image or video sequence. Humans have the ability to recognize objects with bare minimal effort, even though an image varies in different viewpoints. The image also varies when it is translated, scaled, and rotated. People are able to recognize images even when they are somewhat incomplete and missing critical information due to an obstruction of view. Humans use the power of gestalt psychology to do such. Gestalt psychology is defined as a German term interpreted in psychology as a “pattern” or “configuration”.

Gestalt in Practice

Gestalt is based on understanding and perceiving the whole sum of an object rather than its components. This view of psychology was created to go against a belief that scientific understanding is the result of a lack of concern about the basic human details.

The ability for a computer to recognize parts and synthesize them into a larger body object is the main source of error within computer vision and object recognition. This task is extremely challenging for computer vision systems. One must understand that computers have immense capabilities in logically describing constituents or smaller parts, but adding them together consistently to form the basis of a larger item is still difficult. This is personally why I am not too worried about a robot takeover anytime soon. Many approaches to the task have been implemented over multiple decades.

Matlab and object detection/recognition

For a computer to do sufficient object recognition there needs to be a ton of precision with identifying constituent parts. To do this, a computer relies on a vast amount of point cloud data. A point cloud is defined as a set of data points in space. Point clouds are usually produced by 3D scanners. With this point cloud data, metrology, and 3D builds can be created. An object can be recognized through using point cloud data to create a mesh. For us as humans, we are able to interpret that mesh within our 3D realm. However, computers are not that great at such interpretation. They just give us great and precise data to work with. It is important to note that computers are okay at object detection. This refers to being able to decipher a part or object within a larger scene. But when we place multiple parts into a scene or an item with a complex geometry, things become difficult for a computer to decipher. Hence we only use 3D scanners to grab point cloud data and not process what a 3D object is.

Currently in terms of object recognition, computers can barely recognize larger scale items within a 2D setting. It will take a long time for computers to have the graphic capabilities to even decipher what an object would be in a 3D environment. For example, MATLAB is a powerful coding software used for large scale data processing, but computers require a large amount of machine learning and deep learning techniques to process 2D images. First these systems need to do this at a rate of 99.9% confidence before one can move on to 3D images. Humans are not necessarily 100% accurate in terms of processing images either, but they are still slightly more consistent than computer vision techniques. Overall I am interested in learning how to develop such technologies, and I wonder who are the people and organizations wrestling with these problems daily.

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What is Metrology Part 8: Complex Analysis, Optics, and Metrology

The field of metrology is interesting for me as it integrates a lot of what I enjoy in physics and technology. The field from the outside seems very bland, but when you delve into the background, it becomes a more colorful picture. The field is reliant on the physics behind optics and image processing. These are areas of extreme interest to me. Visualization and capturing visualization data is essential for the field. A lot of this data is difficult to interact with as well because the data must be interpreted as a function that can be manipulated for reconstruction purposes from point cloud data. The mathematics behind this is what can be referred to a complex analysis. Today I will give some basic insight into these advanced concepts of physics and how they open us to learning more about metrology and 3D scanning.

Let’s first talk about the field of optics. Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

Optical science is studied in many related disciplines including astronomy, various engineering fields, photography, and medicine. Practical applications of optics are found in a variety of technologies and everyday objects, including mirrors, lenses, telescopes, microscopes, lasers, and fibre optics, as well as metrology practices.

Yes Imaginary Numbers are useful

I personally have a strong fascination with the field of optics. Firstly, I wear glasses and my glasses help me “see” more. The field of optics quickly takes a dive into metaphysical thought processes on human perception as well as what we actually see. Optics is the center of how most of us “see” the world. When we are in the field of metrology we are relying on man-made technology to measure what we see as humans. The realization that we as humans are measuring reality and physical dimensions is a bit mind-boggling. We do not necessarily know what reality is, but we use metrology to measure for us what is within our “grasp”.

Here is where it starts to become a bit more interesting. What defines the system we are in as humans who are measuring within their current state of reality? There must be a larger system that allows for this to occur. This is where complex analysis comes into play. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics. As a differentiable function of a complex variable is equal to the sum of its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions).

Complex Analysis 3D Function

For those of you intimidated by math, I will explain the meaning behind the math. Complex analysis is the branch of mathematics that is trying to understand the imaginary or complex plane of the universe we are confined to. We are working within 3 degrees of freedom or 3-dimensionality within our universe. The system of the universe is not determined by what is seen in the 3-dimensional world. Our perception is not what easily moves the universe. The forces that work on our 3-dimensional universe are applied through the fourth dimension or the complex plane of the universe. For all those who want to learn more physics be sure to enjoy immense philosophical implications. So why is all of this relevant to metrology and optics? Think about this. The signals or data we receive from viewing images is distorted by the complex realm. If it was not, there would be extremely high resolution images taken on a consistent basis. That tiny bit of blur in a photo, for example, is a byproduct of the complex world interacting with the physical realm we are within. This is what typically creates a noisy signal typically in physics. In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion. Noise reduction, the recovery of the original signal from the noise-corrupted one, is a very common goal in the design of signal processing systems, especially filters. The mathematical limits for noise removal are set by information theory, namely the Nyquist–Shannon sampling theorem.

The data we are collecting, or information, is prone to noise. We live in the 3rd dimensions and the complex plane consistently is interacting with our signals or data. Thus we use filters to help with noise cancellation. This is the basis of image processing and digital image reconstruction. The algorithms being created currently for photogrammetric filters are extremely vital for the future of 3D reconstruction. These filters will rely heavily on the field of complex analysis to build better filters. Then we will have very clean 3D reconstructions from our metrology practices. For all those who are intrigued, I will continue to explain different items within the 3D metrology field.

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