Fundamentals Series: Basic Microscopy Calculator

Written by Sias Jordaan

December 9, 2019

Basic calculations are quite handy when you are planning a new or modified imaging setup. Some of these formulas can be found online or in assigned textbooks and you may even find a couple of calculators on websites. However, to simplify this process for you and reduce the time spent hunting for these formulas and worrying whether you’ve got it right, we have gathered the necessary information into a single ready-to-use spreadsheet.

Please leave us a comment if you think there are any glaring omissions.

 

If, after using our calculator, you are still unsure as to which parts will best suit your experimental requirements, please get in touch, and we will assist you every step of the way through our great Bespoke Rig Design service.

The concept of this service stemmed from our slogan – MCI Neuroscience: With Neuroscientists – from Application to Publication, and it entails a comprehensive process where our skilled applications team look into your every experimental requirement, compare the most suitable components, report on the pros and cons of each of their features and ultimately in gathering information, supplier quotes and checking for compatibility of complete systems, for your peace of mind. We not only provide you with the best technology options on the market, but are able to provide you with top quality cost-effective alternatives, through our partnerships with various engineers and researchers. To learn more on how this service could be beneficial to your research, please click on the banner below:

 

Click on the image below to open the MCI Microscopy Calculator:

If you scroll down you will find a glossary of terminology and variables, mainly focused on the numbers necessary as input on the calculator. There’s also an explanation of where to find these variables.

It’s not necessary to read through the glossary before using the calculator – simply hover over the variables in the downloadable file, to display the concepts as explained below.

 

Please note that it will be necessary to add ALL the variables for the different fields on the input side of the calculator

 

The calculator includes the following outputs:

  • Maximum microscope spatial resolution (in transmitted and reflected/fluorescence mode)
  • Objective maximum field of view
  • After-magnification maximum
  • Field of view surface area through eyepieces
  • Field of view diameter through eyepieces
  • Total magnification on monitor via camera stream
  • Total magnification through eyepieces
  • Camera sensor size (width and height)
  • Camera field of view (width, height, diagonal)
  • Camera sensor size
  • Effective pixel size
  • Minimum threshold for camera resolution
  • Surface area of camera field of view

 

 

 

 

GLOSSARY:

 

Objective Design Magnification (printed on objective)

This is usually indicated on the objective barrel as depicted in the image below (4x; 10x; 40x etc). It can also be indicated with a colour code ring around the barrel (to distinguish between objectives when the magnification factor faces away from the operator –  black means 1-1.5x, brown means 2x or 2.5x, red means 4x or 5x, yellow means 10x, green means 16x or 20x, turquoise means 25x or 32x, light blue means 40x or 50x, bright blue means 60x or 63x and white or off-white means 100-250x)

MCI Pryer – Endoscopic objective with a bright blue colour band (as it is closest to the 60x and 63x models) and the 70X printed on the barrel

 

Effective Objective Magnification

Objective magnification is a product of the objective magnification and the specification of the tube lens. If an objective is used with a tube lens with a different focal length from that specified by the manufacturer, this will affect the effective objective magnification.

In the calculator you must therefore enter the focal length of the tube lens on your system. This can be found on the spreadsheet, in table 1 below the calculator

 

Objective Numerical Aperture

The simple explanation of numerical aperture is that it determines the “light capturing capacity” of the objective. It is therefore important to use a high N.A. objective when you’re short on photons in your sample, or when you need high resolution.

The numerical aperture is also printed on the side of the objective barrel. To achieve the specified N.A. you must use the prescribed medium (so oil for oil immersion objectives etc). Objective lenses are complex optical assemblies, and not all manufacturers are exactly accurate with the reported N.A. (sometimes over-reporting slightly).

 

Objective field number

The field number of the objective, together with the magnification, determine the size of the field of view exiting the back aperture of the objective.

This field (the objective’s maximum field of view) is usually not the biggest restriction in the optical path in terms of field of view detected via either the eyes, camera or another detector. But if optimizing field of view is important for your experiment, the objective maximum field of view would be the upper limit – this is calculated in the spreadsheet, using the field number (with other variables).

Some manufacturers print the field number (indicated as F.N.) on the objective barrel. But you’ll often have to dig deeper and do an online specification search or request the field number from the manufacturer.

 

Condenser Numerical Aperture

The concept here is the same as for the objective numerical aperture, but in practice only becomes interesting to the user when in transmitted light mode (there are some exceptions, which we won’t discuss here). The rule of thumb is that, when in transmitted light mode, the condenser N.A. needs to be equal to or exceed the N.A. of the objective.

It is not unusual to have an adjustable numerical aperture on the condenser, and the value is usually indicated on the condenser housing.

 

Eyepieces magnification

Eyepiece magnification, together with the objective effective magnification, determines the total magnification projected onto the eye.

It is usually indicated on the side of the eyepieces (with 10x and 15x being quite common).

 

Eyepiece field number (F.N.)

This determines the maximum field of view observable through the eyepieces. It’s good practice to have this closely match the objective field number, but there may be other apertures and bottlenecks in the light path which may reduce the total field size which can be observed via the eyepieces.

 

Camera pixel size (in x or width and y or height)

This is usually indicated on the camera spec sheet (can usually be found online). Pixels are often square, so if there’s only a single number indicated as the pixel size, it’s safe to assume that both x and y share the same dimension.

Pixel size closely correlates with the spatial resolution which can be processed and displayed by the camera.

 

Camera pixel number (in x or width and y or height)

This is usually indicated on the camera spec sheet (can usually be found online). Camera sensors are often rectangular, with the x-dimension larger compared to y.

More pixels of a fixed dimension translate to a larger chip size, a larger sensor area and therefore a larger field of view on the camera.

 

Digital zoom factor (factor of zoom on computer monitor)

Most camera software packages offer the option of zooming into the image and streaming the zoomed image. Under certain conditions, the operator may need to zoom in for certain observations (for example when patching onto small structures or when using lower magnification objectives).

Depending on the camera’s resolution (along with some other variables), digital zoom may not be an option because of resolution dropping off and pixilation becoming an issue. This empty magnification threshold is calculated in the calculator.

For entering zoom factor, you may need to rely on an estimate, since some software packages don’t display the zoom factor.

 

Auxiliary lenses for additional magnification/demagnification

There are three levels at which additional lenses are typically added to the light path to alter the image magnification (often called “after-magnification/demagnification”).

This can be done by adding a fixed lens or with a switchable lense/s (e.g. magnification changer turrets or sliders). The level where the lens is added has some implications, but in the context of the calculator we’re mainly concerned with its impact on image magnification and resolution, and the fact that you can have more than one level of after-magnification on the same system.

Figure 1: The three different levels of auxiliary lenses

Imaging wavelength (approximation in transmitted light mode)

This variable is used for calculating resolution. When using unfiltered white light in transmitted light mode, you have a wide range for wavelengths combined. In order to calculate resolution, you therefore have to choose a “representative” wavelength. A good option would be blue as an estimate (enter 450nm).

When switching to infra-red mode, for the sake of calculating resolution, you can use the middle of the band if using a bandpass filter for filtering the infra-red. If you’re using a long-pass filter, use a wavelength a few nanometer longer than the cut-off (e.g. when using an 850nm long-pass filter, enter 860nm in the calculator field)

 

Emission wavelength (peak in reflected light mode)

For the sake of resolution calculation, choosing a representative wavelength is easier since you’re targeting a certain band of reflected light. You can enter a value in the middle of the reflected light band into this field on the calculator.

 

Camera window stream dimensions. Refers to the window size of the camera stream on the computer monitor (diagonal)

Camera software allow for streaming a certain window size on the monitor. Some software packages enable the user to stretch this window to fill the monitor completely. Assuming the computer graphics card is not a bottleneck in terms of resolution processing, this dimension considers the camera and the rest of the system’s resolution and is used to calculate resolution on the computer monitor.

 

Focal length of the tube lens which the objective was designed for (see table 1)

This value should be read off the included table, just below the variable input fields. Enter the value for the objective brand.

 

Focal Length of Tube Lens (or trinocular/binocular tube) used on the Microscope, (see table 1)

Again, this should be read off the table, determined by the brand of the tube lens. If you have a binocular or trinocular head on your microscope, the tube lens is built into the unit.

 

CALCULATED VARIABLES

 

  • Effective Pixel Size – Change in pixel size due to (de)magnification factor from auxillary lenses.

Recalculated pixel size with after-magnification elements considered. This is used in calculating camera resolution.

 

  • Camera resolution with Nyquist (this needs to be equal to or smaller than the max achievable resolution of the microscope. If not, you are losing resolution via the camera feed)

The camera resolution is determined mainly by the pixel size, with the after-magnification factor changing the effective pixel size. This value needs to be equal to or smaller than the microscope’s resolution.

 

  • Max pixel size before losing resolution (The max size of your effective pixel size before loosing resolution)

When planning which camera to buy, you can use this value as the top pixel size threshold before losing resolution. This value is calculated for transmitted light mode (enter your expected reflected light value into the transmitted light slot if you want to check this value in reflected light). It also does not consider after-magnification.