Imaging a dense nanodot assembly by phase retrieval from TEM images

Area of Science:

• Physics
• Materials Science
• Microscopy

Background:

• Phase retrieval is a critical inverse problem in wave-based imaging.
• Its application in transmission electron microscopy (TEM) is gaining traction.
• Non-interferometric methods offer potential advantages for TEM phase retrieval.

Purpose of the Study:

• To apply and evaluate a non-interferometric phase retrieval approach for TEM images.
• To compare the transport intensity equation with the weak phase object approximation for phase retrieval.
• To assess the method's accuracy using silicon nanodots and compare with atomic force microscopy.

Main Methods:

• A non-interferometric phase retrieval technique was applied to TEM images.
• The transport intensity equation and weak phase object approximation were compared.
• Image processing in Fourier space was used to solve for phase from defocus images.
• An iterative phase retrieval method was employed to test working conditions.

Main Results:

• Both transport intensity equation and weak phase object approximation yield similar equations for phase retrieval under small-angle approximation.
• The image processing method provides phase images with resolution dependent on defocus amount.
• Height measurements of silicon nanodots using phase images closely matched atomic force microscopy results.
• Image noise and large defocus values were identified as potential limitations for the approximate method.

Conclusions:

• The approximate phase retrieval method is effective for TEM imaging and can be performed with standard equipment.
• The method provides accurate quantitative measurements, demonstrated by silicon nanodot height analysis.
• Iterative methods may be necessary to overcome limitations posed by noise and large defocus values in practical applications.