AFM image reconstruction based on probe parameter estimation and multi-scale feature fusion

Objective Atomic Force Microscope (AFM) is an ultra-high-precision measuring instrument for characterizing surface topography at the nanoscale, and it is widely used in the field of micro/nanotechnology. AFM typically employs a micrometer-length cantilever with a nanoscale sharp probe, enabling nanometer-level lateral resolution and sub-angstrom vertical resolution. When the probe tip approaches the sample surface, interaction forces between them cause the cantilever to bend or alter its vibration frequency, thereby generating two-dimensional or three-dimensional images. However, due to the finite dimensions of the probe tip's geometric structure, morphological distortions occur during the scanning of samples with high-aspect-ratio features, resulting in broader or blurred features in the image compared to the actual profile. This phenomenon is a morphological distortion that arises during scanning. When the radius of curvature of the probe tip is comparable to the geometric features of the sample, the morphological distortion becomes more pronounced and directly affects the measurement results of AFM images.

Methods This paper proposes a method for atomic force microscopy (AFM) image reconstruction based on probe parameter estimation and multi-scale feature fusion. The approach employs a staged optimization strategy within a deep learning-based encoder-decoder architecture (Fig.2). First, a convolutional neural network directly regresses the physical geometric parameters of the probe from input images. Subsequently, a multi-scale U-Net backbone network performs conditional image reconstruction, where the estimated probe parameters serve as critical conditional information to guide the reconstruction process through feature modulation mechanisms. The proposed method is validated on a simulated dataset and demonstrates superior performance compared to conventional methods (Fig.3). It effectively estimates probe parameters while simultaneously improving image reconstruction quality and measurement accuracy (Tab.1). Furthermore, experimental measurements are conducted on two types of rectangular grating standard samples (Fig.7). The relative errors in linewidth, groove depth, and nominal dimensions between reconstructed images, original images, and reference values are calculated and compared, ultimately verifying the applicability and accuracy of the proposed methodology (Tab.3).

Results and Discussions According to the probe parameter estimation results, the estimated tip radius errors for sample 1, sample 2, and sample 3 are 0.8%, 10.0%, and 5.9% respectively, while the cone angle errors are 12.2%, 3.2%, and 11.5% respectively (Fig.4). The proposed method achieves a Mean Absolute Error of Radius (MAE_R) of 2.002 nm and a Root Mean Square Error of Radius (RMSE_R) of 2.407 nm for the test dataset, along with a Mean Absolute Error of cone angle (MAE_a) of 3.704° and a Root Mean Square Error of cone angle (RMSE_a) of 4.252° (Fig.5). These simulation results demonstrate superior performance compared to both the edge reversal method and the blind probe reconstruction method.The AFM image reconstruction results obtained through the proposed method show a Mean Square Error (MSE) of 0.0011, a Peak Signal-to-Noise Ratio (PSNR) of 29.72, and a Structural Similarity Index (SSIM) of 0.889 6. The relative error in linewidth is 1.1% and the error in groove depth is 2.4%, all of which outperform traditional algorithms (Tab.2). These findings validate the effectiveness and applicability of the proposed method.Experimental measurements conducted on two types of standard rectangular gratings reveal that the estimated probe tip radius and cone angle are 11.6 nm and 22.3° respectively, showing excellent agreement with the actual probe parameters (Fig.7). Furthermore, the relative errors in linewidth and groove depth in the reconstructed images are reduced by more than 1.6% and 2.6% respectively compared to the original images (Tab.3). The proposed method not only effectively estimates probe parameters but also significantly eliminates morphological distortions in scanned images, leading to substantially improved measurement accuracy.

Conclusions This paper addresses the morphological distortions occurring during AFM scanning by proposing an AFM image reconstruction method based on probe parameter estimation and multi-scale feature fusion. Experimental results on simulated datasets demonstrate that the proposed method effectively estimates probe parameters with higher accuracy than conventional approaches. Comparative evaluation of AFM image reconstruction quality confirms the robustness and applicability of the method for image restoration.Furthermore, measurement experiments on standard rectangular grating samples show that the proposed method provides probe parameter estimates closely matching the actual values while partially eliminating morphological distortions in scanned images. The relative errors in linewidth and groove depth between the reconstructed images and nominal values are significantly reduced compared to those of the original images, indicating substantially improved measurement accuracy. The integration of this method with commercial AFM imaging software demonstrates considerable potential for practical applications and provides a valuable foundation for further research in this field.