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Related Concept Videos

Common Leveling Mistakes and Errors01:17

Common Leveling Mistakes and Errors

A survey team is tasked with determining the elevation difference between points Point A and Point B, separated by uneven terrain. They use a leveling instrument and a leveling rod.Common MistakesMisreading the Rod: During a backsight reading at Point A, the instrumentman observes the rod partially obscured by tall grass. Instead of reading 1.135 m, they mistakenly record 1.735 m due to the misalignment of the crosshair with the wrong graduation. This error adds 0.600 m to all subsequent...
Errors and Mistakes in Surveying01:19

Errors and Mistakes in Surveying

Errors and mistakes in surveying refer to inaccuracies in measurements and data recording. The errors are deviations from the actual value caused by human sensory limitations, equipment flaws, or environmental effects. These errors are typically unintentional and can result from the inherent imperfections in the instruments used, atmospheric conditions, or the observer’s inability to perceive exact measurements. On the other hand, mistakes are caused by the surveyor's lack of attention,...
Influence of Earth's Curvature and Atmospheric Refraction on Leveling01:26

Influence of Earth's Curvature and Atmospheric Refraction on Leveling

During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference. When the line of sight is leveled, it remains perpendicular to the plumb line only at a single point. Beyond this, it deviates due to the Earth’s curvature, represented by the correction C. For a sight distance D, the deviation can be derived using the relationship:This relationship shows that the deviation increases quadratically with distance. Over a...
Errors in Global Positioning System01:26

Errors in Global Positioning System

Global Positioning System (GPS) technology has revolutionized navigation and positioning, but its accuracy is often compromised by various errors. These errors, stemming from environmental, satellite, and receiver-related factors, require careful mitigation to ensure reliable performance across applications.Atmospheric ErrorsGPS signals travel through the Earth’s ionosphere and troposphere, introducing delays which affect accuracy. The ionosphere is strongly influenced by charged particles,...
Errors in Taping01:18

Errors in Taping

Errors in taping arise from multiple factors that can significantly impact measurement accuracy in surveying. Misalignment of the tape, often due to human error, is one primary source. A skilled rear tapeman, using a telescope, can help correct alignment by guiding the head tapeman; however, human limitations still lead to small inaccuracies. These errors may include misplacement of pins or inaccurate tape readings due to common visual confusions, such as mistaking a six for a nine. Such...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...

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Related Experiment Video

Updated: Jul 6, 2026

Medical-grade Sterilizable Target for Fluid-immersed Fetoscope Optical Distortion Calibration
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Medical-grade Sterilizable Target for Fluid-immersed Fetoscope Optical Distortion Calibration

Published on: February 23, 2017

Simple Estimates for the Effects of Mid-spatial-Frequency Surface Errors on Image Quality.

R N Youngworth, B D Stone

    Applied Optics
    |March 18, 2008
    PubMed
    Summary

    Manufacturing processes can introduce mid-spatial-frequency surface errors in optical systems. A new statistical method predicts their impact on optical performance, offering insights beyond traditional ray tracing.

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    Quantifying Intermembrane Distances with Serial Image Dilations
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    Published on: September 28, 2018

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    Last Updated: Jul 6, 2026

    Medical-grade Sterilizable Target for Fluid-immersed Fetoscope Optical Distortion Calibration
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    Quantifying Intermembrane Distances with Serial Image Dilations
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    Published on: September 28, 2018

    Area of Science:

    • Optical engineering
    • Surface metrology
    • Statistical optics

    Background:

    • Mid-spatial-frequency (MSF) surface errors are common in optics manufacturing.
    • These errors fall between traditional figure and finish error categories.
    • Existing ray-tracing models offer limited insight into MSF error effects.

    Purpose of the Study:

    • To present an alternative method for analyzing MSF surface errors.
    • To enable simple predictions of MSF error impact on optical performance.
    • To provide a statistical approach for understanding these errors.

    Main Methods:

    • Treating surface errors as perturbations to the nominal surface profile.
    • Applying standard statistical methods to analyze these perturbations.
    • Developing a predictive model for optical performance measures.

    Main Results:

    • The proposed method provides a novel way to model MSF errors.
    • It allows for "back-of-the-envelope" predictions of performance impacts.
    • Two illustrative examples demonstrate the method's effectiveness.

    Conclusions:

    • The statistical perturbation method offers valuable insights into MSF errors.
    • This approach complements traditional optical system modeling.
    • It aids in predicting and mitigating the effects of MSF errors in optical design.