Method for Determining the Transfer Function of a Signal Processing System Without Known Input Signal

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The invention describes a method for determining the transfer function (response) of a signal-processing system—such as an imaging device or sensor—even when the input signal is unknown. By using at least two different representations (like images or recordings) of the same or similar object, which are taken at different scales or enlargements, the system's transfer function can be derived mathematically. This is achieved by transforming the representations (typically via Fourier transform), extracting corresponding sections, forming a quotient, and then analyzing the result to determine the system's behavior. The process minimizes reliance on test objects or known input signals, enabling 'blind' characterization of complex systems, such as electron microscopes, where suitable test objects are not available.

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• Calibration and correction of electron microscopes and other imaging systems where test objects are unavailable or impractical.
• Quality control and performance verification of sensors and signal-processing devices without the need for precise input signals.
• Retrospective enhancement and analysis of archived or legacy scientific images and data.
• Improving image and signal analysis in scientific instrumentation (e.g., telescopes, cameras, spectrometers).
• Robust system characterization for medical imaging devices where controlled test inputs are difficult to realize.
• Use in any signal capture system (audio, video, instrumentation) to measure system response without dedicated calibration objects.

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• Enables accurate determination of a system’s transfer function without the need for a known input signal or special calibration targets.
• Applicable to many types of signal-processing systems (imaging, audio, measurement systems, etc.).
• Can improve the quality and reliability of data and images by enabling better correction and deconvolution.
• Allows retrospective calibration of old or historical data, unlocking new insights from archival material.
• Reduces the costs and effort of calibration by removing the requirement for physical test objects or point sources.
• Supports automation and robustness in system setup and maintenance, especially for systems with variable or difficult-to-control environments.

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Patent Abstract

The invention relates to methods for determining the transfer function of a signal-processing system, which do not presuppose a known input signal. The methods are based on two representations I1(x) and I2(x) of an object which have been produced by the system from differently scaled input signals originating from the object, or from a representation I1(x) of a first object and from a representation I2(x) of an object which is geometrically similar thereto but has been scaled differently. The representations are either given or are produced at the start of the method. According to the invention, the representations are transformed into a working space, and sections which relate to the same region of the object are selected in each case. The quotient of the functions corresponding to these two sections in the working space from which the unknown input signal comes makes it possible to clearly determine the transfer function sought. Different methods are stated for this determination. The method can be used, in particular, to improve the images from electron microscopes for which there are no suitable test structures for determining the transfer function.