Mary Cooper Scott
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Mary Cooper Scott has a total of 292 co-authors. Here are the top co-authors by number of shared publications:
- Colin Ophus
Stanford University
12 shared publications - Ellis Kennedy
Los Alamos National Laboratory
9 shared publications - Gerbrand Ceder
Department of Materials Science and Engineering University of California Berkeley California USA
8 shared publications - Luis Rangel DaCosta
Department of Materials Science and Engineering, University of California, Hearst Memorial Mining Building, Berkeley, CA 94720, USA
8 shared publications - Ali Javey
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA
6 shared publications - Georgios Varnavides
University of California, Berkeley
5 shared publications
Latest Publications
- Open Access
- 8 September 2026
- Published by Oxford University Press (OUP) in Microscopy and Microanalysis
- Vol. 32 (5)
Sodium Expulsion From Sodium closo -Hydroborates Under Electron Beam-Induced Bias
Electron microscopy invites the opportunity to locally characterize the properties of solid-state electrolytes important for choreographing ion motion within next-generation solid-state batteries. Through the combination of inert gas transfer, cryogenic, time-resolved low-dose analytical electron microscopy, we observe that mixed-anion sodium closo-hydroborate, Na2(B10H10)0.5(B12H12)0.5 (NBH), solid electrolyte suffers from electrostatic charging damage under bias in both transmission electron microscopes and scanning electron microscopes (SEM). During the process of beam damage, crystalline ordering of NBH is lost, while particle morphology remains unchanged. In regions exposed to electron beams at a dose rate of 1–8 e− Å−2 s−1, spectroscopy confirms a vastly reduced sodium signal or even sodium absence from irradiated NBH at total doses less than 80 e− Å−2. Simultaneously, we detect the growth of sodium metal crystals on the unirradiated faces of NBH particles. An SEM experimental study revealed that the maximum damage rate occurs at 2 keV, with increasing energy prolonging the time before sodium is emitted. This work also highlights that cryogenic conditions, while highly effective in mitigating certain types of inelastic beam damage, are not the solution for reducing beam sensitivity. Rather, comprehensive awareness of the underlying physics in competing damage mechanisms is paramount in the selection of operating conditions for battery interface characterization.
- 8 September 2026
- Published by Oxford University Press (OUP) in Microscopy and Microanalysis
- Vol. 32 (5)
Open AccessSodium Expulsion From Sodium closo -Hydroborates Under Electron Beam-Induced Bias
Electron microscopy invites the opportunity to locally characterize the properties of solid-state electrolytes important for choreographing ion motion within next-generation solid-state batteries. Through the combination of inert gas transfer, cryogenic, time-resolved low-dose analytical electron microscopy, we observe that mixed-anion sodium closo-hydroborate, Na2(B10H10)0.5(B12H12)0.5 (NBH), solid electrolyte suffers from electrostatic charging damage under bias in both transmission electron microscopes and scanning electron microscopes (SEM). During the process of beam damage, crystalline ordering of NBH is lost, while particle morphology remains unchanged. In regions exposed to electron beams at a dose rate of 1–8 e− Å−2 s−1, spectroscopy confirms a vastly reduced sodium signal or even sodium absence from irradiated NBH at total doses less than 80 e− Å−2. Simultaneously, we detect the growth of sodium metal crystals on the unirradiated faces of NBH particles. An SEM experimental study revealed that the maximum damage rate occurs at 2 keV, with increasing energy prolonging the time before sodium is emitted. This work also highlights that cryogenic conditions, while highly effective in mitigating certain types of inelastic beam damage, are not the solution for reducing beam sensitivity. Rather, comprehensive awareness of the underlying physics in competing damage mechanisms is paramount in the selection of operating conditions for battery interface characterization.
- Open Access
- 1 July 2026
- Published by Oxford University Press (OUP) in Microscopy and Microanalysis
- Vol. 32 (4)
Contrast Transfer Functions Help Quantify Neural Network Out-Of-Distribution Generalization in HRTEM.
Neural networks, while effective for tackling many challenging scientific tasks, are not known to perform well out-of-distribution (OOD), i. within domains which differ from their training data. Understanding neural network OOD generalization is paramount to their successful deployment in experimental workflows, especially when ground-truth knowledge about the experiment is hard to establish or experimental conditions significantly vary. With inherent access to ground-truth information and fine-grained control of underlying distributions, simulation-based data curation facilitates precise investigation of OOD generalization behavior. Here, we probe generalization with respect to imaging conditions of neural network segmentation models for high-resolution transmission electron microscopy (HRTEM) imaging of nanoparticles, training and measuring the OOD generalization of over 12,000 neural networks using synthetic data generated via random structure sampling and multislice simulation. Using the HRTEM contrast transfer function, we further develop a framework to compare information content of HRTEM datasets and quantify OOD domain shifts. We demonstrate that neural network segmentation models enjoy significant performance stability, but will smoothly and predictably worsen as imaging conditions shift from the training distribution. Lastly, we consider limitations of our approach in explaining other OOD shifts, such as of the atomic structures, and discuss complementary techniques for understanding generalization in such settings.
- 1 July 2026
- Published by Oxford University Press (OUP) in Microscopy and Microanalysis
- Vol. 32 (4)
Open AccessContrast Transfer Functions Help Quantify Neural Network Out-Of-Distribution Generalization in HRTEM.
Neural networks, while effective for tackling many challenging scientific tasks, are not known to perform well out-of-distribution (OOD), i. within domains which differ from their training data. Understanding neural network OOD generalization is paramount to their successful deployment in experimental workflows, especially when ground-truth knowledge about the experiment is hard to establish or experimental conditions significantly vary. With inherent access to ground-truth information and fine-grained control of underlying distributions, simulation-based data curation facilitates precise investigation of OOD generalization behavior. Here, we probe generalization with respect to imaging conditions of neural network segmentation models for high-resolution transmission electron microscopy (HRTEM) imaging of nanoparticles, training and measuring the OOD generalization of over 12,000 neural networks using synthetic data generated via random structure sampling and multislice simulation. Using the HRTEM contrast transfer function, we further develop a framework to compare information content of HRTEM datasets and quantify OOD domain shifts. We demonstrate that neural network segmentation models enjoy significant performance stability, but will smoothly and predictably worsen as imaging conditions shift from the training distribution. Lastly, we consider limitations of our approach in explaining other OOD shifts, such as of the atomic structures, and discuss complementary techniques for understanding generalization in such settings.
- Open Access
- 3 March 2026
- Published by Oxford University Press (OUP) in Microscopy and Microanalysis
- Vol. 32 (2)
Beyond Contrast Transfer: Spectral SNR as a Finite-Dose Metric for STEM Phase Retrieval
The contrast transfer function (CTF) is widely used to evaluate phase retrieval methods in scanning transmission electron microscopy (STEM), including center-of-mass imaging, parallax imaging, direct ptychography, and iterative ptychography. However, the CTF reflects only the maximum usable signal, neglecting the effects of finite electron fluence and the Poisson-limited nature of detection. As a result, it can significantly overestimate practical performance, especially in low-dose regimes. Here, we employ the spectral signal-to-noise ratio (SSNR), as a finite-dose statistical framework to evaluate the recoverable signal as a function of spatial frequency. Using numerical reconstructions of white-noise objects, we show that center-of-mass, parallax, and direct ptychography exhibit dose-independent SSNRs, with close-form analytic expressions. In contrast, iterative ptychography exhibits a surprising dose dependence: at low fluence, its SSNR converges to that of direct ptychography; at high fluence, it saturates at a value consistent with the maximum detective quantum efficiency predicted by recent quantum Fisher information bounds. The results highlight the limitations of CTF-based evaluation and motivate SSNR as a more accurate, finite-dose metric for assessing STEM phase retrieval methods.
- 3 March 2026
- Published by Oxford University Press (OUP) in Microscopy and Microanalysis
- Vol. 32 (2)
Open AccessBeyond Contrast Transfer: Spectral SNR as a Finite-Dose Metric for STEM Phase Retrieval
The contrast transfer function (CTF) is widely used to evaluate phase retrieval methods in scanning transmission electron microscopy (STEM), including center-of-mass imaging, parallax imaging, direct ptychography, and iterative ptychography. However, the CTF reflects only the maximum usable signal, neglecting the effects of finite electron fluence and the Poisson-limited nature of detection. As a result, it can significantly overestimate practical performance, especially in low-dose regimes. Here, we employ the spectral signal-to-noise ratio (SSNR), as a finite-dose statistical framework to evaluate the recoverable signal as a function of spatial frequency. Using numerical reconstructions of white-noise objects, we show that center-of-mass, parallax, and direct ptychography exhibit dose-independent SSNRs, with close-form analytic expressions. In contrast, iterative ptychography exhibits a surprising dose dependence: at low fluence, its SSNR converges to that of direct ptychography; at high fluence, it saturates at a value consistent with the maximum detective quantum efficiency predicted by recent quantum Fisher information bounds. The results highlight the limitations of CTF-based evaluation and motivate SSNR as a more accurate, finite-dose metric for assessing STEM phase retrieval methods.
- Open Access
- 24 December 2025
- Published by Microscopy Society of America
Strategies for effective transfer learning for HRTEM analysis with neural networks
Transfer learning provides a practical opportunity to adapt machine learning models to new domains by retraining models on a new, typically smaller set of data. This technique is especially useful for supervised learning problems in electron microscopy, where high-quality, labeled experimental data are scarce and experimental conditions can change significantly across experiments. Using simulated benchmark datasets, we investigate a series of transfer learning protocols for developing segmentation models for locating nanoparticles in high-resolution transmission electron microscopy ( HRTEM ) data. We train over 10,500 neural networks and evaluate model performance and out-of-distribution generalization capabilities after both pretraining and transfer learning phases, covering shifts in imaging conditions, noise conditions, and structural distributions. Via our high-throughput data generation and model training approach, we demonstrate that transfer learning can be an effective strategy to tackle domain shifts in machine learning problems for HRTEM and that transfer learning can be beneficial for model generalization. Lastly, we provide some practical training recommendations for adopting transfer learning protocols into machine learning development pipelines.
- 24 December 2025
- Published by Microscopy Society of America
Open AccessStrategies for effective transfer learning for HRTEM analysis with neural networks
Transfer learning provides a practical opportunity to adapt machine learning models to new domains by retraining models on a new, typically smaller set of data. This technique is especially useful for supervised learning problems in electron microscopy, where high-quality, labeled experimental data are scarce and experimental conditions can change significantly across experiments. Using simulated benchmark datasets, we investigate a series of transfer learning protocols for developing segmentation models for locating nanoparticles in high-resolution transmission electron microscopy ( HRTEM ) data. We train over 10,500 neural networks and evaluate model performance and out-of-distribution generalization capabilities after both pretraining and transfer learning phases, covering shifts in imaging conditions, noise conditions, and structural distributions. Via our high-throughput data generation and model training approach, we demonstrate that transfer learning can be an effective strategy to tackle domain shifts in machine learning problems for HRTEM and that transfer learning can be beneficial for model generalization. Lastly, we provide some practical training recommendations for adopting transfer learning protocols into machine learning development pipelines.
- Open Access
- 17 December 2025
- Published by Springer Nature in Nature Communications
- Vol. 17 (1)
PhaseT3M: 3D imaging at 1.6 Å resolution via electron cryo-tomography with nonlinear phase retrieval
Electron cryo-tomography (cryo-ET) enables 3D imaging of complex, radiation-sensitive structures with molecular detail. However, image contrast from the interference of scattered electrons is nonlinear with atomic density and multiple scattering further complicates interpretation. These effects degrade resolution, particularly in conventional reconstruction algorithms, which assume linearity. Particle averaging can reduce such issues but is unsuitable for heterogeneous or dynamic samples ubiquitous in biology, chemistry, and materials sciences. Here, we develop a phase retrieval-based cryo-ET method, PhaseT3M. We experimentally demonstrate its application to an approximately 7 nm Co3O4 nanoparticle on an approximately 30 nm carbon substrate, achieving a maximum resolution of 1.6 Å, surpassing conventional limits using standard cryo-TEM equipment. PhaseT3M uses a multislice model for multiple scattering and Bayesian optimization for alignment and computational aberration correction, with a positivity constraint to recover ‘missing wedge’ information. Applied directly to biological particles, it enhances reconstruction quality and reduces artifacts, establishing a standard for routine 3D imaging with phase contrast.
- 17 December 2025
- Published by Springer Nature in Nature Communications
- Vol. 17 (1)
Open AccessPhaseT3M: 3D imaging at 1.6 Å resolution via electron cryo-tomography with nonlinear phase retrieval
Electron cryo-tomography (cryo-ET) enables 3D imaging of complex, radiation-sensitive structures with molecular detail. However, image contrast from the interference of scattered electrons is nonlinear with atomic density and multiple scattering further complicates interpretation. These effects degrade resolution, particularly in conventional reconstruction algorithms, which assume linearity. Particle averaging can reduce such issues but is unsuitable for heterogeneous or dynamic samples ubiquitous in biology, chemistry, and materials sciences. Here, we develop a phase retrieval-based cryo-ET method, PhaseT3M. We experimentally demonstrate its application to an approximately 7 nm Co3O4 nanoparticle on an approximately 30 nm carbon substrate, achieving a maximum resolution of 1.6 Å, surpassing conventional limits using standard cryo-TEM equipment. PhaseT3M uses a multislice model for multiple scattering and Bayesian optimization for alignment and computational aberration correction, with a positivity constraint to recover ‘missing wedge’ information. Applied directly to biological particles, it enhances reconstruction quality and reduces artifacts, establishing a standard for routine 3D imaging with phase contrast.
- Open Access
Contrast transfer functions help quantify neural network out-of-distribution generalization in HRTEM
Neural networks, while effective for tackling many challenging scientific tasks, are not known to perform well out-of-distribution (OOD), i.e., within domains which differ from their training data. Understanding neural network OOD generalization is paramount to their successful deployment in experimental workflows, especially when ground-truth knowledge about the experiment is hard to establish or experimental conditions significantly vary. With inherent access to ground-truth information and fine-grained control of underlying distributions, simulation-based data curation facilitates precise investigation of OOD generalization behavior. Here, we probe generalization with respect to imaging conditions of neural network segmentation models for high-resolution transmission electron microscopy (HRTEM) imaging of nanoparticles, training and measuring the OOD generalization of over 12,000 neural networks using synthetic data generated via random structure sampling and multislice simulation. Using the HRTEM contrast transfer function, we further develop a framework to compare information content of HRTEM datasets and quantify OOD domain shifts. We demonstrate that neural network segmentation models enjoy significant performance stability, but will smoothly and predictably worsen as imaging conditions shift from the training distribution. Lastly, we consider limitations of our approach in explaining other OOD shifts, such as of the atomic structures, and discuss complementary techniques for understanding generalization in such settings.
Open AccessContrast transfer functions help quantify neural network out-of-distribution generalization in HRTEM
Neural networks, while effective for tackling many challenging scientific tasks, are not known to perform well out-of-distribution (OOD), i.e., within domains which differ from their training data. Understanding neural network OOD generalization is paramount to their successful deployment in experimental workflows, especially when ground-truth knowledge about the experiment is hard to establish or experimental conditions significantly vary. With inherent access to ground-truth information and fine-grained control of underlying distributions, simulation-based data curation facilitates precise investigation of OOD generalization behavior. Here, we probe generalization with respect to imaging conditions of neural network segmentation models for high-resolution transmission electron microscopy (HRTEM) imaging of nanoparticles, training and measuring the OOD generalization of over 12,000 neural networks using synthetic data generated via random structure sampling and multislice simulation. Using the HRTEM contrast transfer function, we further develop a framework to compare information content of HRTEM datasets and quantify OOD domain shifts. We demonstrate that neural network segmentation models enjoy significant performance stability, but will smoothly and predictably worsen as imaging conditions shift from the training distribution. Lastly, we consider limitations of our approach in explaining other OOD shifts, such as of the atomic structures, and discuss complementary techniques for understanding generalization in such settings.
- Open Access
Investigating the Degradation of LATP Solid Electrolyte in High Alkaline Li-$O_2$ Batteries
In this study, we address the challenge of electrolyte degradation in all-solid-state humidified Li-$O_2$ batteries, which offer high theoretical energy density and potential cost advantages over conventional lithium-ion batteries. Combining STEM-EELS, and XPS characterizations with DFT calculations, we reveal the leaching of $(PO_4)^{3+}$ and $Al^{3+}$ ions from the $Li_{1.3}Al_{0.3}Ti_{1.7}(PO_4)_3$ (LATP) solid electrolyte upon battery discharge, caused by the highly alkaline environment. Upon charging, the leached ions precipitate as $Li_3PO_4$ and $AlPO_4$, which accumulate on the LATP surface and contribute to battery degradation. A Ti-rich layer is observed at the surface after a few cycles due to depletion of other cations. Our findings suggest that the degradation products are formed through repeated dissolution and precipitation in the discharge-charge cycles. Furthermore, our results indicate that the Ti-rich layer on the LATP surface can potentially reduce parasitic reactions. Our study provides mechanistic understanding of LATP solid electrolyte degradation in humidified Li-$O_2$ cell, paving the way for designing more durable and efficient Li-$O_2$ batteries.Open AccessInvestigating the Degradation of LATP Solid Electrolyte in High Alkaline Li-$O_2$ Batteries
In this study, we address the challenge of electrolyte degradation in all-solid-state humidified Li-$O_2$ batteries, which offer high theoretical energy density and potential cost advantages over conventional lithium-ion batteries. Combining STEM-EELS, and XPS characterizations with DFT calculations, we reveal the leaching of $(PO_4)^{3+}$ and $Al^{3+}$ ions from the $Li_{1.3}Al_{0.3}Ti_{1.7}(PO_4)_3$ (LATP) solid electrolyte upon battery discharge, caused by the highly alkaline environment. Upon charging, the leached ions precipitate as $Li_3PO_4$ and $AlPO_4$, which accumulate on the LATP surface and contribute to battery degradation. A Ti-rich layer is observed at the surface after a few cycles due to depletion of other cations. Our findings suggest that the degradation products are formed through repeated dissolution and precipitation in the discharge-charge cycles. Furthermore, our results indicate that the Ti-rich layer on the LATP surface can potentially reduce parasitic reactions. Our study provides mechanistic understanding of LATP solid electrolyte degradation in humidified Li-$O_2$ cell, paving the way for designing more durable and efficient Li-$O_2$ batteries. - 1 August 2025
- Published by Springer Nature in Nature Materials
- Vol. 25 (1) , 18-25
Memsensing by surface ion migration within Debye length
Integration between electronics and biology is often facilitated by iontronics, where ion migration in aqueous media governs sensing and memory. However, the Debye screening effect limits electric fields to the Debye length, the distance over which mobile ions screen electrostatic interactions, necessitating external voltages that constrain the operation speed and device design. Here we report a high-speed in-memory sensor based on vanadium dioxide (VO2) that operates without an external voltage by leveraging built-in electric fields within the Debye length. When VO2 contacts a low-work-function metal (for example, indium) in a salt solution, electrochemical reactions generate indium ions that migrate into the VO2 surface under the native electric field, inducing a surface insulator-to-metal phase transition of VO2. The VO2 conductance increase rate reflects the salt concentration, enabling in-memory sensing, or memsensing of the solution. The memsensor mimics Caenorhabditis elegans chemosensory plasticity to guide a miniature boat for adaptive chemotaxis, illustrating low-power aquatic neurorobotics with fewer memory units.
- 1 August 2025
- Published by Springer Nature in Nature Materials
- Vol. 25 (1) , 18-25
Memsensing by surface ion migration within Debye length
Integration between electronics and biology is often facilitated by iontronics, where ion migration in aqueous media governs sensing and memory. However, the Debye screening effect limits electric fields to the Debye length, the distance over which mobile ions screen electrostatic interactions, necessitating external voltages that constrain the operation speed and device design. Here we report a high-speed in-memory sensor based on vanadium dioxide (VO2) that operates without an external voltage by leveraging built-in electric fields within the Debye length. When VO2 contacts a low-work-function metal (for example, indium) in a salt solution, electrochemical reactions generate indium ions that migrate into the VO2 surface under the native electric field, inducing a surface insulator-to-metal phase transition of VO2. The VO2 conductance increase rate reflects the salt concentration, enabling in-memory sensing, or memsensing of the solution. The memsensor mimics Caenorhabditis elegans chemosensory plasticity to guide a miniature boat for adaptive chemotaxis, illustrating low-power aquatic neurorobotics with fewer memory units.
- Open Access
- 1 June 2025
- Published by Wiley in Advanced Energy Materials
- Vol. 15 (30)
Mitigating Battery Cell Failure: Role of Ag‐Nanoparticle Fillers in Solid Electrolyte Dendrite Suppression
The development of solid‐state batteries (SSBs) with lithium Li metal anodes holds significant promise for enhancing the energy density and safety of next‐generation energy storage systems. However, their commercialization is hindered by challenges related to Li dendrite formation, which can lead to short circuits and battery failure. In this study, the role of Ag nanoparticles embedded within solid electrolytes (SE) is investigated in suppressing dendrite propagation. The results demonstrate that Ag nanoparticles effectively mitigate two key failure mechanisms: (1) dendrite growth within porous networks at low current densities and (2) stress intensification‐induced SE fracture at higher current densities (12 mA cm−2). Ex situ characterization using focused‐ion beam – scanning electron microscopy (FIB–SEM) and energy dispersive X‐ray spectroscopy (EDS,) reveals that Ag nanoparticles migrate alongside advancing Li dendrites, promoting homogeneous dendrite growth and reducing the likelihood of localized stress concentrations. Additionally, the incorporation of Ag nanoparticles is shown to facilitate a more uniform Li distribution toward the anode side, which can potentially enable the use of higher charging rates in SSBs. This study provides a new perspective on Li dendrite suppression and presents new opportunities for enhancing the performance and safety of SSBs.
- 1 June 2025
- Published by Wiley in Advanced Energy Materials
- Vol. 15 (30)
Open AccessMitigating Battery Cell Failure: Role of Ag‐Nanoparticle Fillers in Solid Electrolyte Dendrite Suppression
The development of solid‐state batteries (SSBs) with lithium Li metal anodes holds significant promise for enhancing the energy density and safety of next‐generation energy storage systems. However, their commercialization is hindered by challenges related to Li dendrite formation, which can lead to short circuits and battery failure. In this study, the role of Ag nanoparticles embedded within solid electrolytes (SE) is investigated in suppressing dendrite propagation. The results demonstrate that Ag nanoparticles effectively mitigate two key failure mechanisms: (1) dendrite growth within porous networks at low current densities and (2) stress intensification‐induced SE fracture at higher current densities (12 mA cm−2). Ex situ characterization using focused‐ion beam – scanning electron microscopy (FIB–SEM) and energy dispersive X‐ray spectroscopy (EDS,) reveals that Ag nanoparticles migrate alongside advancing Li dendrites, promoting homogeneous dendrite growth and reducing the likelihood of localized stress concentrations. Additionally, the incorporation of Ag nanoparticles is shown to facilitate a more uniform Li distribution toward the anode side, which can potentially enable the use of higher charging rates in SSBs. This study provides a new perspective on Li dendrite suppression and presents new opportunities for enhancing the performance and safety of SSBs.
- Open Access
- 14 May 2025
- Published by Microscopy Society of America
Evaluating the Transfer of Information in Phase Retrieval STEM Techniques
Phase retrieval methods in scanning transmission electron microscopy (STEM) recover scattered phase information from far-field intensity measurements of a converged electron probe. We evaluate the performance of various phase retrieval techniques – including center-of-mass imaging (COM), tilt-corrected bright-field STEM (tcBF), and direct ptychographic methods such as single-side band (SSB) and Wigner distribution deconvolution (WDD) – under different experimental conditions. Through analytical derivation of contrast transfer functions (CTF) under the weak phase-object approximation and numerical validation using white-noise samples, we assess the impact of scan sampling, illumination aberrations, and detector geometries. Based on these findings, we develop a novel direct ptychographic algorithm that combines the relaxed scan-sampling advantages of tcBF while avoiding CTF zero-crossings through SSB recovery. Our analysis reveals fundamental limitations in using CTF as a performance metric and demonstrates the advantages of dose-invariant spectral signal-to-noise ratio (SSNR) for evaluating phase retrieval methods.
- 14 May 2025
- Published by Microscopy Society of America
Open AccessEvaluating the Transfer of Information in Phase Retrieval STEM Techniques
Phase retrieval methods in scanning transmission electron microscopy (STEM) recover scattered phase information from far-field intensity measurements of a converged electron probe. We evaluate the performance of various phase retrieval techniques – including center-of-mass imaging (COM), tilt-corrected bright-field STEM (tcBF), and direct ptychographic methods such as single-side band (SSB) and Wigner distribution deconvolution (WDD) – under different experimental conditions. Through analytical derivation of contrast transfer functions (CTF) under the weak phase-object approximation and numerical validation using white-noise samples, we assess the impact of scan sampling, illumination aberrations, and detector geometries. Based on these findings, we develop a novel direct ptychographic algorithm that combines the relaxed scan-sampling advantages of tcBF while avoiding CTF zero-crossings through SSB recovery. Our analysis reveals fundamental limitations in using CTF as a performance metric and demonstrates the advantages of dose-invariant spectral signal-to-noise ratio (SSNR) for evaluating phase retrieval methods.