Uncertainty Calculator vs Microscope Resolution

Uncertainty Calculator evaluates the error propagation throughout the mathematical expressions comprised of variables of uncertain value. The application allows input of up to three value-error pairs (A, B and C), that can be used as a parameters in the final expression. Error values should be provided in absolute (100 +/- 5) or in relative format, the latter should appear in percent format (100 +/- 5%). The evaluated expression can include numerous functions, that provided by row of the appropriate buttons. Components and functions can be added directly to the expression field by pressing the corresponding buttons. To encompass expression into the preset formula, select the expression and press the corresponding formula button. Particular attention should be paid to placing brackets to avoid equation ambiguity. The application deals with independent, random errors. So if this is a case never use A + A, but rather 2*A and never A*A*A but rather A^3! Obviously, different parameters can be combined in any way (A+B or C *A^2 .. is perfectly fine). Angles for trigonometric functions can be provided in degrees or radians, and that should be reflected by setting a yellow button to "DEG" or "RAD". Bear in mind the importance of units in any of calculations! Implementation Examples: 1.The charge passing through an electrical circuit is defined by: Q = I * t, where I is the current and t is the time. Calculate the total charge value when a current of 0.15 ± 0.01 A passes through the circuit for 120 ± 1 s: Input: A = 0.15 ± 0.01, B = 120 ± 1 The final expression will be A*B, and press Calculate: The final value will be: 18 ± 1.2 Thus, it can be reported the total charge as 18 C ± 1 C. Important! One should only report as many significant figures as are consistent with estimated error! So the value should be rounded to the rightmost decimal place at which error applies. 2. A ball is tossed straight up into the air with initial speed vo = (4.0± 0.2) m/s. After a time t = (0.60 ± 10%) s, the height of the ball is h = vo*t - 0.5gt^2 = 0.636 m (g = 9.80 m/s^2). What is the value and uncertainty of height? Input: A = vo = 4.0 ± 0.2, and B = t = 0.60 ± 10%, then the final expression should be: A*B – 0.5*9.8*B^2 The final value will be: 0.6 ± 0.4 (meters).

Characterize your microscope objective lenses, see how well matched they are to your microscope's image acquisition system. The App supports both transmitted light objectives and fluorescence objectives. Input the magnification, immersion medium (air, oil, glycerol or silicone oil), NA (numerical aperture), condenser NA and wavelength of light (lambda), to calculate the lateral resolution, axial resolution and brightness of the objective. Characterize your acquisition system (camera pixel size, camera binning and additional magnification) to check if you're sampling at Nyquist frequency. Each of your objectives can be saved and easily restored, and shared with other microscopists via e-mail, MMS, Linked-In or even Facebook. The equations used for the calculations can be displayed. The sources of equations are referenced in the "Information" section. * Theoretical Resolution is calculated according Ernst Abbe's famous equation (Abbe 1873) * Actual Resolution is calculated according to ‘The Rayleigh Criterion’ * Axial Resolution of fluorescence objectives is calculated according to Inoue's chapter in Jim Pawley's “Handbook of Biological Confocal Microscopy” (3rd edition 2006) * Camera pixel size can be loaded from the list of cameras, if your camera is not in the list, you can enter it manually. * Select the "share" feature to share all output to e-mail, MMS or Linked-In * It doesn't matter if your microscope was made by Zeiss, Evos, Leica, Olympus, Nikon, Motic, or Meiji Techno, the principles are identical and you will find the app useful. * The list of cameras in the Camera dialog includes those made by Andor, Hamamatsu, Photometrics, PCO, QImaging, Leica, Lumenera, Olympus, Nikon, Motic and Zeiss.