Improving DQE with Counting and Super-Resolution

Counting                         Super-resolution

For over 20 years, Gatan has continued to improve our cameras for transmission electron microscopy (TEM). While there are many ways to characterize the performance of an imaging device, detective quantum efficiency (DQE), is the most reliable indicator of resolution for low dose imaging.

DQE measures the combined signal effects (related to image resolution and contrast) and noise performance of an imaging system that vary with spatial frequency. It describes how effectively the camera can produce an image with a high signal-to-noise ratio (SNR). DQE is a good indicator for how much data is obtained per unit of electron dose to the sample. Mathematically DQE is expressed as the relationship between the output and input of the SNR.

DQE = (SNRout)2 / (SNRin)2

If a specimen is imaged with a detector that only has 33% DQE, the result will be noisier than the original, and many of the high resolution details will be lost.

Detector with DQE
of 33%

Note image details, such as the eyes, hair and nose that are lost by a detector with a low DQE.

 

To overcome this challenge, continuous DQE improvement led to the K2 Summit® camera; which offers the highest DQE of any TEM camera to date. K2 Summit camera includes traditional integration, electron counting and super-resolution electron counting modes.

Traditional integration

Similar to indirect detection cameras, direct detectors can integrate the total charge produced when an electron strikes a pixel. These detectors are most commonly used for high dose applications. While direct detectors offer an increase in DQE, in integration mode they do not remove read noise or the variation in signal that is dependent on the electron interaction with the detector.

     

Counting

In counting mode, individual electron events are identified at the time that they reach the detector. To do this efficiently the camera must run fast enough so that individual electron events can be identified separately.

A benefit of counting is that it rejects signal read noise and variability associated with electron scattering, while it dramatically lifts the detector's DQE across all spatial frequencies.

The K2 Summit electron counting mode replaces the analog signal from each primary electron with a discrete count.

        

Counting electrons compared to counting raindrops on the sidewalk (pavement)

Using the analogy of counting raindrops (left) compared to electrons (right), electron counting is only possible if the camera can read-out images fast enough to “see” the individual electrons "raining" down on the sensor.

If the electrons are "raining" quickly, the camera needs a high frame rate in order to count individual electrons.

 

When compared to traditional integration (left), counting removes the variability from scattering, rejects the electronic read noise, and restores the DQE (right).

 

Super-resolution

The theoretical information limit defined by the physical pixel size is surpassed when you use the K2 in super-resolution mode. The K2 sensor pixel size is slightly smaller than the area that the electron interacts with; as a result each incoming electron deposits signal in a small cluster of pixels. High-speed electronics are able to recognize each electron event (at 400 fps) and find the center of event with sub-pixel precision.

The net effect is a 4x improvement in effective number of pixels (beyond the physical Nyquist limit), as well as a further improvement of the DQE.

         

 

 

The difference between counting and super-resolution DQE, as shown in the graph, is mainly due to noise present in the counted images that is caused by aliasing. The largest advantage of super-resolution is that it minimizes this effect.