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I'm evaluating a sigma lens that comes in several mounts including aps-c and micro four-thirds. My question is about the performance on the smaller micro four-thirds sensor. Couldn't I expect the performance to be superior as the smaller sensor would only utilize the center of the image Circle? many thanks

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The only way to know how a lens and camera body will perform together is to test them together.

  • While a smaller sensor will crop out the edges and corners of the image, which do tend to have poorer image quality (by whatever metric), not all lenses suffer equally from the same problems. A very good lens with good corner and edge sharpness won't see any improvement from cropping.

  • By cropping out part of the image in camera, you reduce your ability to crop the image yourself in post.

  • Some imperfections may be desirable (aberrations and vignetting that help emphasize the subject). Cropping them out would be undesirable.

  • Using a smaller sensor effectively "magnifies" the center of the image (when printed or viewed at the same size). Imperfections that may go unnoticed when a lens used with larger sensors may become obvious when used with smaller sensors.

    • The resolution of a lens may not be high enough to produce a sharp image on a smaller sensor.

    • Chromatic aberrations may be more visible.

  • Smaller sensors can introduce their own problems because they may cram more pixels into the same unit area.

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Short Answer

You usually gain a bit from cropping out the edges of the image circle.¹

You always lose a bit by increasing the magnification ratio to display the image from a smaller sensor at the same size as you would display the image from a larger sensor.

Which way the combination of both together tilts is entirely dependent upon the specific lens, the two specific sensors/cameras involved, the shooting conditions, etc.

¹ This is more the case with very wide, very fast prime lenses or zoom lenses that include wide angles of view or very broad focal length ranges, such as an 18-200mm, than it is with prime lenses longer than a camera's sensor diagonal measurement. For APS-C and FF cameras, prime lenses longer than about 70mm show very little vignetting, distortion, lower resolution, etc. at the edges. Telephoto zoom lenses with limited focal length ranges, such as 70-200mm lenses, also demonstrate the same aberrations much less than typical zooms in the wide angle ranges, such as a 16-35mm or 17-50mm.


Long Answer

A camera is a tool. Tools come in different shapes and sizes. Some are better suited for using one way for certain tasks. Other tools are better suited for using other ways to do other tasks.

In general larger sensors allow the possibility of better image quality, but they in no way guarantee it. Sometimes the difference in quality will be incremental and hardly even noticeable. Sometimes it will be quite obvious. Often the other things needed to allow using the larger sensor to get that quality means spending a lot more money on things such as lenses in addition to the higher initial cost of the larger sensor.

Where larger sensors have greater advantages:

  • The magnification needed to view the virtual image, as projected onto the sensor, at a specific size is smaller for a larger sensor compared to a smaller one. This means the flaws projected by the lens aren't as magnified when the image is viewed. To get the same sharpness with a smaller sensor, the lens must also be sharper.
  • Since exposure is measured as the amount of light per unit area, larger sensors collect more total light for the same exposure value. This trends to make larger sensors less noisy. The age of the sensor's technology can also affect this to a significant degree. But if two sensors from the same manufacturer use the same generation of technology the larger one will almost always be less noisy when shooting the same scene with the same settings and then viewing both at the same size.
  • Larger sensors tend to have larger photosites which are also known as pixel cells or sensels. Because a larger photosite has more surface area, it can collect more photons before it reaches full well capacity. This gives sensors with larger photosites more dynamic range. DR is the difference between the brightest value a sensor can record and the dimmest value that can be recorded and still be discriminated from noise. This is one reason why larger sensors are less noisy than smaller sensors.
  • Since lenses of the same focal length will give a wider angle of view when used with a larger sensor, it is easier and less costly to make wide angle lenses for larger sensors.

Where smaller sensors have greater advantages:

  • The magnification needed to view the virtual image, as projected onto the sensor, at a specific size is larger for a smaller sensor compared to a larger one. This means a lens with a specific focal length will give greater "reach" with a smaller sensor than a larger sensor. Things the same distance from the camera will appear larger with a smaller sensor than on a larger one when the same focal length is used with each and the respective images are then viewed at the same display size.

  • Since aperture is expressed as a ratio of the focal length to the diameter of the entrance pupil, shorter focal length lenses can achieve the same exposure or f-number with a smaller aperture diameter than a longer focal length lens. If a larger sensor needs a 100mm focal length for a certain angle of view and a smaller sensor only needs a 50mm focal length to give the same angle of view, the smaller lens can have an entrance pupil half as wide and give the same f-number as the longer lens.

  • Since lenses of the same focal length will give a narrower angle of view when used with a smaller sensor, it is easier and less costly to make telephoto lenses for smaller sensors.

In the end, the quality of a tool is only as good as the skill of the one who is using the tool. Only when the tool is limiting the skill set of the user will a better tool make a difference.


Further Reading

For far more extensive discussions of the differences between using the same lenses on larger and smaller sensors (usually couched in 'FF' vs. 'APS-C', but the differences also apply to any two different sensor format sizes), please see these questions here at Photo.SE:

With all other things equal, in a DSLR, will a larger sensor produce a sharper image?
Given the same lens, does shooting with FX cameras yield sharper results than DX cameras?
Why is FF sharper than crop body for the same framing of the same object?
What Do I Gain from Moving to a Full-Frame DSLR?
Why does it seem like large sensors are necessary for good low-light performance?
Do full frame sensors have a higher exposure?
Does sensor size impact the diffraction limit of a lens?
Why are larger sensors better at low light?
What is the visual difference between Full Frame, APS-C and Micro Four Thirds pictures?
When do the differences between APS-C and full frame sensors matter, and why?
Full Frame Vs Crop Frame
Is the low-light advantage of larger sensors attributable to the sensor itself or to the larger aperture of the lenses?
Do I need a full-frame camera for low-light photography?
How does the smaller mirror in APS-C cameras offer these advantages?
What significant improvement will I get if I upgrade to Canon EOS 6D from EOS APSC 600D?
How does sensor size impact depth of field and diffraction for macro photography?
6D or 80D for upgrade from 100D?
Big sensor and landscape photography, DoF
Can we always talk about noise difference between crop and full frame?
Fancy technology cropped vs old technology full frame - Which will give better images?
Is small sensor always a bad thing?
Does sensor size affect lens distortion?
Which sensor "full frame" vs. APS-C (1.6 crop) gives more distortion?
This recent answer to this older question: Are full-frame cameras bad for sports photography?

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