Standard Deviation by Linear Function of Camera Exposure Time Calculator

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Digital Image Fundamentals

Intensity Transformation

✖Model Function : function used to model the behavior of Σ with IRED.ⓘ Model Function [ζ]			+10% -10%
✖radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle.ⓘ Radiant Intensity [I_p]			+10% -10%
✖Model Behaviour Function is the function to model the behavior with distance d between the camera and the IRED.ⓘ Model Behaviour Function [δ]			+10% -10%
✖Distance between Camera and the IRED.ⓘ Distance between Camera and the IRED [d]			+10% -10%
✖Model Coefficient 1 the coefficient to model the linear relationship between t and Σ.ⓘ Model Coefficient 1 [τ₁]			+10% -10%
✖Camera Exposure Time :the length of time the camera collects light from your sample.ⓘ Camera Exposure Time [t]			+10% -10%
✖Model Coefficient 2 is the coefficient to model the linear relationship between t and Σ.ⓘ Model Coefficient 2 [τ₂]			+10% -10%

✖The standard deviation provides a measure of the dispersion of image gray level intensities and can be understood as power level of the alternating signal component acquired by the camera.ⓘ Standard Deviation by Linear Function of Camera Exposure Time [Σ]

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Formula

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Standard Deviation by Linear Function of Camera Exposure Time

Formula

`"Σ" = "ζ"*("I"_{"p"})*"δ"*(1/"d"^2)*("τ"_{"1"}*"t"+"τ"_{"2"})`

Example

`"87.09663"="1.75"*("2.45mA")*"6"*(1/("2.85cm")^2)*("3.15"*"6μs"+"2.75")`

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Standard Deviation by Linear Function of Camera Exposure Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Deviation = Model Function*(Radiant Intensity)*Model Behaviour Function*(1/Distance between Camera and the IRED^2)*(Model Coefficient 1*Camera Exposure Time+Model Coefficient 2)
Σ = ζ*(I_p)*δ*(1/d^2)*(τ₁*t+τ₂)
This formula uses 8 Variables

Variables Used

Standard Deviation - The standard deviation provides a measure of the dispersion of image gray level intensities and can be understood as power level of the alternating signal component acquired by the camera.
Model Function - Model Function : function used to model the behavior of Σ with IRED.
Radiant Intensity - (Measured in Ampere) - radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle.
Model Behaviour Function - Model Behaviour Function is the function to model the behavior with distance d between the camera and the IRED.
Distance between Camera and the IRED - (Measured in Meter) - Distance between Camera and the IRED.
Model Coefficient 1 - Model Coefficient 1 the coefficient to model the linear relationship between t and Σ.
Camera Exposure Time - (Measured in Second) - Camera Exposure Time :the length of time the camera collects light from your sample.
Model Coefficient 2 - Model Coefficient 2 is the coefficient to model the linear relationship between t and Σ.

STEP 1: Convert Input(s) to Base Unit

Model Function: 1.75 --> No Conversion Required
Radiant Intensity: 2.45 Milliampere --> 0.00245 Ampere (Check conversion here)
Model Behaviour Function: 6 --> No Conversion Required
Distance between Camera and the IRED: 2.85 Centimeter --> 0.0285 Meter (Check conversion here)
Model Coefficient 1: 3.15 --> No Conversion Required
Camera Exposure Time: 6 Microsecond --> 6E-06 Second (Check conversion here)
Model Coefficient 2: 2.75 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Σ = ζ*(I_p)*δ*(1/d^2)*(τ₁*t+τ₂) --> 1.75*(0.00245)*6*(1/0.0285^2)*(3.15*6E-06+2.75)

Evaluating ... ...

Σ = 87.0966281348107

STEP 3: Convert Result to Output's Unit

87.0966281348107 --> No Conversion Required

FINAL ANSWER

87.0966281348107 ≈ 87.09663 <-- Standard Deviation

(Calculation completed in 00.004 seconds)

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Created by Surya Tiwari

Punjab Engineering College (PEC), Chandigarh, India

Surya Tiwari has created this Calculator and 9 more calculators!

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Chandigarh University (CU), Punjab

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< 19 Digital Image Fundamentals Calculators

Standard Deviation by Linear Function of Camera Exposure Time

Go Standard Deviation = Model Function*(Radiant Intensity)*Model Behaviour Function*(1/Distance between Camera and the IRED^2)*(Model Coefficient 1*Camera Exposure Time+Model Coefficient 2)

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Cumulative Frequency for Each Brightness Value

Go Cumulative Frequency for Each Brightness Value = 1/Total Number of Pixels*sum(x,0,Maximum Brightness Value,Frequency of Occurence of Each Brightness Value)

Run-Length Entropy of Image

Go Run Length Entropy of Image = (Entropy of Black Run Length+Entropy of White Run Length)/(Average Value of Black Runlength+Average Value of White Runlength)

Linear Combination of Expansion

Go Linear Combination of expansion functions = sum(x,0,Integer Index For Linear Expansion,Real Valued Expansion Coefficients*Real Valued Expansion Functions)

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Go Detail Wavelet Coefficient = int(Scaling Function Expansion*Wavelet Expansion Function*x,x,0,Integer Index For Linear Expansion)

Quantization Step Size in Image Processing

Go Quantization Step Size = (2^(Nominal Dynamic Range-Number of Bits Alloted to Exponent))*(1+Number of Bits Alloted to Mantissa/2^11)

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Image File Size

Go Image File Size = Image Resolution*Bit Depth/8000

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Go Energy of Component = [hP]*Frequency

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Go Number of Grey Level = 2^Digital Image Column

Standard Deviation by Linear Function of Camera Exposure Time Formula

Definition of Standard Deviation ?

The standard deviation (Σ) provides a measure of the dispersion of image gray level intensities and can be understood as a measure of the power level of the alternating signal component acquired by the camera. Therefore, a relationship would exist between the standard deviation and the camera exposure time, IRED radiant intensity and distance, assuming that the IRED and the camera are aligned.

How to Calculate Standard Deviation by Linear Function of Camera Exposure Time?

Standard Deviation by Linear Function of Camera Exposure Time calculator uses Standard Deviation = Model Function*(Radiant Intensity)*Model Behaviour Function*(1/Distance between Camera and the IRED^2)*(Model Coefficient 1*Camera Exposure Time+Model Coefficient 2) to calculate the Standard Deviation, The Standard Deviation by linear function of camera exposure time. shows that standard deviation can be modeled by a linear function of camera exposure time. where ζ is the function used to model the behavior of Σ with IRED radiant intensity Ip, δ is the function to model the behavior with distance d between the camera and the IRED, and τ1 and τ2 are the coefficients to model the linear relationship between t and Σ. Standard Deviation is denoted by Σ symbol.

How to calculate Standard Deviation by Linear Function of Camera Exposure Time using this online calculator? To use this online calculator for Standard Deviation by Linear Function of Camera Exposure Time, enter Model Function (ζ), Radiant Intensity (I_p), Model Behaviour Function (δ), Distance between Camera and the IRED (d), Model Coefficient 1 (τ₁), Camera Exposure Time (t) & Model Coefficient 2 (τ₂) and hit the calculate button. Here is how the Standard Deviation by Linear Function of Camera Exposure Time calculation can be explained with given input values -> 87.09663 = 1.75*(0.00245)*6*(1/0.0285^2)*(3.15*6E-06+2.75).

FAQ

What is Standard Deviation by Linear Function of Camera Exposure Time?

The Standard Deviation by linear function of camera exposure time. shows that standard deviation can be modeled by a linear function of camera exposure time. where ζ is the function used to model the behavior of Σ with IRED radiant intensity Ip, δ is the function to model the behavior with distance d between the camera and the IRED, and τ1 and τ2 are the coefficients to model the linear relationship between t and Σ and is represented as Σ = ζ*(I_p)*δ*(1/d^2)*(τ₁*t+τ₂) or Standard Deviation = Model Function*(Radiant Intensity)*Model Behaviour Function*(1/Distance between Camera and the IRED^2)*(Model Coefficient 1*Camera Exposure Time+Model Coefficient 2). Model Function : function used to model the behavior of Σ with IRED, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, Model Behaviour Function is the function to model the behavior with distance d between the camera and the IRED, Distance between Camera and the IRED, Model Coefficient 1 the coefficient to model the linear relationship between t and Σ, Camera Exposure Time :the length of time the camera collects light from your sample & Model Coefficient 2 is the coefficient to model the linear relationship between t and Σ.

How to calculate Standard Deviation by Linear Function of Camera Exposure Time?

The Standard Deviation by linear function of camera exposure time. shows that standard deviation can be modeled by a linear function of camera exposure time. where ζ is the function used to model the behavior of Σ with IRED radiant intensity Ip, δ is the function to model the behavior with distance d between the camera and the IRED, and τ1 and τ2 are the coefficients to model the linear relationship between t and Σ is calculated using Standard Deviation = Model Function*(Radiant Intensity)*Model Behaviour Function*(1/Distance between Camera and the IRED^2)*(Model Coefficient 1*Camera Exposure Time+Model Coefficient 2). To calculate Standard Deviation by Linear Function of Camera Exposure Time, you need Model Function (ζ), Radiant Intensity (I_p), Model Behaviour Function (δ), Distance between Camera and the IRED (d), Model Coefficient 1 (τ₁), Camera Exposure Time (t) & Model Coefficient 2 (τ₂). With our tool, you need to enter the respective value for Model Function, Radiant Intensity, Model Behaviour Function, Distance between Camera and the IRED, Model Coefficient 1, Camera Exposure Time & Model Coefficient 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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