Image contrast and interpretationTh

Image contrast and interpretation
The contrast of a HRTEM image arises from the interference in the image plane of the electron wave with itself. Due to our inability to record the phase of an electron wave, only the amplitude in the image plane is recorded. However, a large part of the structure information of the sample is contained in the phase of the electron wave. In order to detect it, the aberrations of the microscope (like defocus) have to be tuned in a way that converts the phase of the wave at the specimen exit plane into amplitudes in the image plane.

The interaction of the electron wave with the crystallographic structure of the sample is complex, but a qualitative idea of the interaction can readily be obtained. Each imaging electron interacts independently with the sample. Above the sample, the wave of an electron can be approximated as a plane wave incident on the sample surface. As it penetrates the sample, it is attracted by the positive atomic potentials of the atom cores, and channels along the atom columns of the crystallographic lattice (s-state model[4]). At the same time, the interaction between the electron wave in different atom columns leads to Bragg diffraction. The exact description of dynamical scattering of electrons in a sample not satisfying the weak phase object approximation (WPOA), which is almost all real samples, still remains the holy grail of electron microscopy. However, the physics of electron scattering and electron microscope image formation are sufficiently well known to allow accurate simulation of electron microscope images.[5]

As a result of the interaction with a crystalline sample, the electron exit wave right below the sample φe(x,u) as a function of the spatial coordinate x is a superposition of a plane wave and a multitude of diffracted beams with different in plane spatial frequencies u (spatial frequencies correspond to scattering angles, or distances of rays from the optical axis in a diffraction plane). The phase change φe(x,u) relative to the incident wave peaks at the location of the atom columns. The exit wave now passes through the imaging system of the microscope where it undergoes further phase change and interferes as the image wave in the imaging plane (mostly a digital pixel detector like a CCD camera). It is important to realize, that the recorded image is NOT a direct representation of the samples crystallographic structure. For instance, high intensity might or might not indicate the presence of an atom column in that precise location (see simulation). The relationship between the exit wave and the image wave is a highly nonlinear one and is a function of the aberrations of the microscope. It is described by the contrast transfer function.
Optimum defocus in HRTEM
To calculate back to φe(x,u) the wave in the image plane is back propagated numerically to the sample. If all properties of the microscope are well known, it is possible to recover the real exit wave with very high accuracy.

First however, both phase and amplitude of the electron wave in the image plane must be measured. As our instruments only record amplitudes, an alternative method to recover the phase has to be used. There are two methods in use today:

Holography, which was developed by Gabor expressly for TEM applications, uses a prism to split the beam into a reference beam and a second one passing through the sample. Phase changes between the two are then translated in small shifts of the interference pattern, which allows recovering both phase and amplitude of the interfering wave.
Through focal series method takes advantage of the fact that the CTF is focus dependent. A series of about 20 pictures is shot under the same imaging conditions with the exception of the focus which is incremented between each take. Together with exact knowledge of the CTF the series allows for computation of φe(x,u) (see figure).
Both methods extend the point resolution of the microscope the information limit, which is the highest possible resolution achievable on a given machine. The ideal defocus value for this type of imaging is known as Lichte defocus and is usually several hundred nanometers negative.

Kết quả (Việt) 1:

Hình ảnh tương phản và giải thíchSự tương phản của hình ảnh HRTEM phát sinh từ sự can thiệp trong mặt phẳng hình ảnh của sóng điện tử với chính nó. Do chúng tôi không có khả năng ghi lại giai đoạn của một làn sóng điện tử, chỉ biên độ trong mặt phẳng hình ảnh được ghi lại. Tuy nhiên, một phần lớn của các thông tin cấu trúc của mẫu được chứa trong giai đoạn đầu của làn sóng điện tử. Để phát hiện nó, quang sai của kính hiển vi (như defocus) phải được điều chỉnh theo cách mà chuyển đổi giai đoạn đầu của làn sóng lúc máy bay lối ra mẫu vào amplitudes trong mặt phẳng hình ảnh.Sự tương tác của sóng điện tử với cấu trúc crystallographic của mẫu là phức tạp, nhưng một ý tưởng về chất lượng của sự tương tác có thể dễ dàng được lấy. Mỗi điện tử hình ảnh tương tác một cách độc lập với mẫu. Trên mẫu, làn sóng một điện tử có thể được ước chừng là một sự cố máy bay sóng trên bề mặt mẫu. Như nó thâm nhập vào mẫu, nó là thu hút bởi tích cực tiềm năng nguyên tử của các nguyên tử lõi, và các kênh dọc theo cột atom của crystallographic lưới (s-nhà nước model[4]). Cùng lúc đó, sự tương tác giữa làn sóng điện tử trong cột khác nhau nguyên tử dẫn đến Bragg nhiễu xạ. Các mô tả chính xác về động lực tán xạ của các điện tử trong một mẫu không đáp ứng xấp xỉ đối tượng yếu giai đoạn (WPOA), mà là gần như tất cả mẫu thực tế, vẫn còn các chén Thánh của kính hiển vi điện tử. Tuy nhiên, vật lý của điện tử tán xạ và kính hiển vi điện tử hình thành hình ảnh đủ cũng được biết đến để cho phép các mô phỏng chính xác của hình ảnh kính hiển vi điện tử. [5]As a result of the interaction with a crystalline sample, the electron exit wave right below the sample φe(x,u) as a function of the spatial coordinate x is a superposition of a plane wave and a multitude of diffracted beams with different in plane spatial frequencies u (spatial frequencies correspond to scattering angles, or distances of rays from the optical axis in a diffraction plane). The phase change φe(x,u) relative to the incident wave peaks at the location of the atom columns. The exit wave now passes through the imaging system of the microscope where it undergoes further phase change and interferes as the image wave in the imaging plane (mostly a digital pixel detector like a CCD camera). It is important to realize, that the recorded image is NOT a direct representation of the samples crystallographic structure. For instance, high intensity might or might not indicate the presence of an atom column in that precise location (see simulation). The relationship between the exit wave and the image wave is a highly nonlinear one and is a function of the aberrations of the microscope. It is described by the contrast transfer function.Optimum defocus in HRTEMTo calculate back to φe(x,u) the wave in the image plane is back propagated numerically to the sample. If all properties of the microscope are well known, it is possible to recover the real exit wave with very high accuracy.First however, both phase and amplitude of the electron wave in the image plane must be measured. As our instruments only record amplitudes, an alternative method to recover the phase has to be used. There are two methods in use today:Holography, which was developed by Gabor expressly for TEM applications, uses a prism to split the beam into a reference beam and a second one passing through the sample. Phase changes between the two are then translated in small shifts of the interference pattern, which allows recovering both phase and amplitude of the interfering wave.Through focal series method takes advantage of the fact that the CTF is focus dependent. A series of about 20 pictures is shot under the same imaging conditions with the exception of the focus which is incremented between each take. Together with exact knowledge of the CTF the series allows for computation of φe(x,u) (see figure).Both methods extend the point resolution of the microscope the information limit, which is the highest possible resolution achievable on a given machine. The ideal defocus value for this type of imaging is known as Lichte defocus and is usually several hundred nanometers negative.