Contrast Transfer Research Articles

Linear imaging theory for differential phase contrast and other phase imaging modes in scanning transmission electron microscopy

We propose a linear imaging theory for differential phase contrast under the weak-phase-weak-amplitude object approximation. Contrast transfer functions are defined for thin and thick weak objects, and they successfully describe several imaging characteristics of differential phase contrast. We discuss the defocus dependence of the contrast for several examples: atomic resolution, a p-n junction, a heterointerface, and grain boundaries. Understanding the imaging characteristics helps in adjusting aberrations in DPC STEM.

High-resolution structure determination using high-throughput electron cryo-tomography.

Tomographic reconstruction of frozen-hydrated specimens followed by extraction and averaging of sub-tomograms has successfully been used to determine the structure of macromolecules in their native environment at resolutions that are high enough to reveal molecular level interactions. The low throughput characteristic of tomographic data acquisition combined with the complex data-analysis pipeline that is required to obtain high-resolution maps, however, has limited the applicability of this technique to favorable samples or to resolutions that are too low to provide useful mechanistic information. Recently, beam image-shift electron cryo-tomography (BISECT), a strategy to significantly accelerate the acquisition of tilt series without sacrificing image quality, was introduced. The ability to produce thousands of high-quality tilt series during a single microscope session, however, introduces significant bottlenecks in the downstream data analysis, which has so far relied on specialized pipelines. Here, recent advances in accurate estimation of the contrast transfer function and self-tuning exposure-weighting routines that contribute to improving the resolution and streamlining the structure-determination process using sub-volume averaging are reviewed. Ultimately, the combination of automated data-driven techniques for image analysis together with high-throughput strategies for tilt-series acquisition will pave the way for tomography to become the technique of choice for in situ structure determination.

Aberration-corrected transmission electron microscopy with Zernike phase plates

We explore the possibility of applying physical phase plates (PPs) in combination with aberration-corrected transmission electron microscopy. Phase-contrast transfer characteristics are calculated and compared for a thin-film based Zernike PP, a hole-free (HF) or Volta PP and an electrostatic Zach PP, considering their phase-shifting properties in combination with partial spatial coherence. The effect of slightly converging illumination conditions, often used in high-resolution applications, on imaging with PPs is discussed. Experiments with an unheated Zernike PP applied to various nanomaterial specimens and a qualitative analysis clearly demonstrates the general compatibility of PPs and aberration-corrected transmission electron microscopy. Calculations and experiments show the benefits of the approach, among which is a strong phase-contrast enhancement of a large range of spatial frequencies. This allows the simultaneous imaging of atomic-resolution structures and morphological features at the nanometer scale, with maximum phase contrast. The calculations can explain why the HFPP damps contrast transfer at higher spatial frequencies.

Mixed scale dense convolutional networks for x-ray phase contrast imaging

X-ray in-line phase contrast imaging relies on the measurement of Fresnel diffraction intensity patterns due to the phase shift and the attenuation induced by the object. The recovery of phase and attenuation from one or several diffraction patterns is a nonlinear ill-posed inverse problem. In this work, we propose supervised learning approaches using mixed scale dense (MS-D) convolutional neural networks to simultaneously retrieve the phase and the attenuation from x-ray phase contrast images. This network architecture uses dilated convolutions to capture features at different image scales and densely connects all feature maps. The long range information in images becomes quickly available, and greater receptive field size can be obtained without losing resolution. This network architecture seems to account for the effect of the Fresnel operator very efficiently. We train the networks using simulated data of objects consisting of either homogeneous components, characterized by a fixed ratio of the induced refractive phase shifts and attenuation, or heterogeneous components, consisting of various materials. We also train the networks in the image domain by applying a simple initial reconstruction using the adjoint of the Fréchet derivative. We compare the results obtained with the MS-D network to reconstructions using U-Net, another popular network architecture, as well as to reconstructions using the contrast transfer function method, a direct phase and attenuation retrieval method based on linearization of the direct problem. The networks are evaluated using simulated noisy data as well as images acquired at NanoMAX (MAX IV, Lund, Sweden). In all cases, large improvements of the reconstruction errors are obtained on simulated data compared to the linearized method. Moreover, on experimental data, the networks improve the reconstruction quantitatively, improving the low-frequency behavior and the resolution.

Integrated Differential Phase Contrast (IDPC)-STEM Utilizing a Multi-Sector Detector for Imaging Thick Samples.

The integrated differential phase contrast (IDPC) method is useful for generating the potential map of a thin sample. We evaluate theoretically the potential of IDPC imaging for thick samples by varying the focus at different sample thicknesses. Our calculations show that high defocus values result in enhanced anisotropy of the contrast transfer function (CTF) and uninterpretable images, if a quadrant detector is applied. We further show that applying a multi-sector detector can result in an almost isotropic CTF. By sector number-dependent calculations for both Cc/C3-corrected and C3-corrected scanning transmission electron microscopy (STEM), we show that the increase of detector sectors not only removes the anisotropy of the CTF, but also improves image contrast and resolution. For a proof-of-principle IDPC-STEM (uncorrected) experiment, we realize the functionality of a 12-sector detector from a physical quadrant detector and demonstrate the improvement in contrast and resolution on the example of InGaN/GaN quantum well structure.

Determination of phases of complex scattering amplitudes and two-particle structure factors by investigating diffractograms of thin amorphous foils

Abstract In this study we analyse diffractograms of elastically filtered images of thin amorphous foils of carbon, silicon and germanium using the weak object approximation. The use of this approximation leads to a contrast transfer function containing a phase η(u) depending on the spatial frequency u. Furthermore, the derivative of this phase is included in the envelope function of the contrast transfer function. The phase can be attributed to the breakdown of the first-order Born approximation leading to complex scattering amplitudes characterized by this phase η(u). We analyse contrast transfer characteristics to determine the phase of complex scattering amplitudes of carbon, silicon and germanium as a function of spatial frequency and to measure the two-particle structure factor of the corresponding amorphous specimens. The contrast transfer characteristics were calculated from diffractograms of focal series of elastically filtered images. The phases measured show a decay with increasing spatial frequency and additional oscillations. The results for the two-particle structure factor also decay with increasing spatial frequency and contain low local maxima. Both can be attributed to voids or inhomogeneities within the amorphous structure.

A generalized framework for the image formation model and disentanglement of CTF parameters in cryo-electron microscopy

In cryo-electron microscopy (cryo-EM), the microscope has a point spread function, whose Fourier transform, known as the Contrast Transfer Function (CTF), is determined by various parameters with a physical meaning (including height of the sample, magnetic lens aberrations, operating voltage, amplitude contrast, etc.). Some of the parameters are under experimental control, but they can also contain some experimental uncertainty and fluctuate over the course of data collection. While it is routine to use point estimates for the CTF parameters in a simplified forward model of image formation, we characterize here the uncertainty of the CTF by (1) framing the forward model of image formation as a probabilistic graphical model, (2) deriving conditional probabilities that leverage analytical linking functions, and (3) compare these results with existing approaches that model noise in frequency space, such as the “B-factor envelope” and the “white/coloured noise model”.

A Robust Single-Particle Cryo-Electron Microscopy (cryo-EM) Processing Workflow with cryoSPARC, RELION, and Scipion.

Recent advances in both instrumentation and image processing software have made single-particle cryo-electron microscopy (cryo-EM) the preferred method for structural biologists to determine high-resolution structures of a wide variety of macromolecules. Multiple software suites are available to new and expert users for image processing and structure calculation, which streamline the same basic workflow: movies acquired by the microscope detectors undergo correction for beam-induced motion and contrast transfer function (CTF) estimation. Next, particle images are selected and extracted from averaged movie frames for iterative 2D and 3D classification, followed by 3D reconstruction, refinement, and validation. Because various software packages employ different algorithms and require varying levels of expertise to operate, the 3D maps they generate often differ in quality and resolution. Thus, users regularly transfer data between a variety of programs for optimal results. This paper provides a guide for users to navigate a workflow across the popular software packages: cryoSPARC v3, RELION-3, and Scipion 3 to obtain a near-atomic resolution structure of the adeno-associated virus (AAV). We first detail an image processing pipeline with cryoSPARC v3, as its efficient algorithms and easy-to-use GUI allow users to quickly arrive at a 3D map. In the next step, we use PyEM and in-house scripts to convert and transfer particle coordinates from the best quality 3D reconstruction obtained in cryoSPARC v3 to RELION-3 and Scipion 3 and recalculate 3D maps. Finally, we outline steps for further refinement and validation of the resultant structures by integrating algorithms from RELION-3 and Scipion 3. In this article, we describe how to effectively utilize three processing platforms to create a single and robust workflow applicable to a variety of data sets for high-resolution structure determination.

Improvement of a floating 3D light field display based on a telecentric retroreflector and an optimized 3D image source

For a floating three-dimensional (3D) display system using a prism type retroreflector, non-retroreflected light and a blurred 3D image source are two key causes of the deterioration in image quality. In the present study, ray tracing is used to analyze the light distribution of a retroreflector at different incident angles. Based on this analysis, a telecentric retroreflector (TCRR) is proposed to suppress non-retroreflected light without sacrificing the viewing angle. A contrast transfer function (CTF) is used to evaluate the optical performance of the TCRR. To improve the 3D image source, the relationship between the root mean square (RMS) of the voxels and the 3D image quality is discussed, and an aspheric lens array is designed to reduce aberrations. Computational simulation results reveal that the structural similarity (SSIM) of the 3D image source increased to 0.9415. An experimental prototype system combining the TCRR and optimized 3D image source is then built. Experimental analysis demonstrates that the proposed method suppresses non-retroreflected light and improves the 3D image source. In particular, a clear floating 3D image with a floating distance of 70 mm and a viewing angle of 50° can be achieved.

Analysis of angular dependent spatial frequency response of Digital Coplanar Translational Laminography

Digital Coplanar Translational Laminography (CTL) is a radiographic imaging technique that permits the visualization of structural details and discontinuities in the object of interest after 3D reconstruction from multiple projections. This technique becomes quite competitive regarding to computed tomography in situations of arrangements in which no complete rotation of the X-ray source - detector system around the object of interest is accessible or in cases where the part to be inspected has a high geometric asymmetry. The literature does not show many studies about image quality for different laminographic reconstructions and scan geometries. Different methodologies for measuring the Modulation Transfer Function (MTF) as a key image quality parameter for the aforementioned technique are applied. The MTF was measured using different approaches, pre-sampled MTF or sampled MTF, both based on the Fourier Transform-Magnitude Spectrum or the square wave MTF using line pattern gauges. A sample known as Siemens Star with a converging line pattern was used to measure the circular square wave MTF. This circular MTF provides information on the direction dependent contrast transfer related to the measurement conditions, the reconstruction algorithms and the translational scan direction. For this purpose, several MTF measurements were performed in multiple angular directions. Beyond it, reconstructions were performed using different algorithms (Filtered Shifted Average) and an iterative one (MART – Multiplicative Algebraic Reconstruction Technique). Image quality analysis were done for both reconstruction methods. MART showed an image quality improvement for challenging conditions for laminographic arrangements, such as for a low number of projections (down to 25 for this study, considered as limited view, limited angle reconstruction). Additionally, a Gadolinium gauge with parallel line patterns within a range from 10 μm to 1000 μm was used to compare the square wave MTF with the sine MTFs, measured by the different techniques mentioned above. The results show that the MTF techniques presented are equivalent in this study. The results obtained for this Gadolinium plate showed a good agreement between MTF10% and SRbimage measurements. The methodology presented here is used for the characterization of the frequency dependent spatial resolution of measurements obtained from different laminographic reconstruction techniques and scan geometries. Finally, from the acquisitions and reconstructions obtained with the Siemens Star, cross laminographic images were calculated in order to improve the direction dependent sensitivity. The results showed a better detectability for cross laminographic images in comparison to unidirectional coplanar translational laminographic images covering dead zones.

Toward Compositional Contrast by Cryo-STEM.

Electron microscopy (EM) is the most versatile tool for the study of matter at scales ranging from subatomic to visible. The high vacuum environment and the charged irradiation require careful stabilization of many specimens of interest. Biological samples are particularly sensitive due to their composition of light elements suspended in an aqueous medium. Early investigators developed techniques of embedding and staining with heavy metal salts for contrast enhancement. Indeed, the Nobel Prize in 1974 recognized Claude, de Duve, and Palade for establishment of the field of cell biology, largely due to their developments in separation and preservation of cellular components for electron microscopy. A decade later, cryogenic fixation was introduced. Vitrification of the water avoids the need for dehydration and provides an ideal matrix in which the organic macromolecules are suspended; the specimen represents a native state, suddenly frozen in time at temperatures below -150 °C. The low temperature maintains a low vapor pressure for the electron microscope, and the amorphous nature of the medium avoids diffraction contrast from crystalline ice. Such samples are extremely delicate, however, and cryo-EM imaging is a race for information in the face of ongoing damage by electron irradiation. Through this journey, cryo-EM enhanced the resolution scale from membranes to molecules and most recently to atoms. Cryo-EM pioneers, Dubochet, Frank, and Henderson, were awarded the Nobel Prize in 2017 for high resolution structure determination of biological macromolecules.A relatively untapped feature of cryo-EM is its preservation of composition. Nothing is added and nothing removed. Analytical spectroscopies based on electron energy loss or X-ray emission can be applied, but the very small interaction cross sections conflict with the weak exposures required to preserve sample integrity. To what extent can we interpret quantitatively the pixel intensities in images themselves? Conventional cryo-transmission electron microscopy (TEM) is limited in this respect, due to the strong dependence of the contrast transfer on defocus and the absence of contrast at low spatial frequencies.Inspiration comes largely from a different modality for cryo-tomography, using soft X-rays. Contrast depends on the difference in atomic absorption between carbon and oxygen in a region of the spectrum between their core level ionization energies, the so-called water window. Three dimensional (3D) reconstruction provides a map of the local X-ray absorption coefficient. The quantitative contrast enables the visualization of organic materials without stain and measurement of their concentration quantitatively. We asked, what aspects of the quantitative contrast might be transferred to cryo-electron microscopy?Compositional contrast is accessible in scanning transmission EM (STEM) via incoherent elastic scattering, which is sensitive to the atomic number Z. STEM can be regarded as a high energy, low angle diffraction measurement performed pixel by pixel with a weakly convergent beam. When coherent diffraction effects are absent, that is, in amorphous materials, a dark field signal measures quantitatively the flux scattered from the specimen integrated over the detector area. Learning to interpret these signals will open a new dimension in cryo-EM. This Account describes our efforts so far to introduce STEM for cryo-EM and tomography of biological specimens. We conclude with some thoughts on further developments.

Differential programming enabled functional imaging with Lorentz transmission electron microscopy

Lorentz transmission electron microscopy is an advanced characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials. Information such as magnetization and electric potentials is carried by the phase of the electron wave, and is lost during image acquisition. Various methods have been proposed to retrieve the phase of the electron wavefunction using intensities of the acquired images, most of which work only in the small defocus limit. Imaging at strong defoci not only carries more quantitative phase information, but is essential to the study of weak magnetic and electrostatic fields at the nanoscale. In this work we develop a method based on differentiable programming to solve the inverse problem of phase retrieval. We show that our method maintains a high spatial resolution and robustness against noise even at the upper defocus limit of the microscope. More importantly, our proposed method can go beyond recovering just the phase information. We demonstrate this by retrieving the electron-optical parameters of the contrast transfer function alongside the electron exit wavefunction.

TomoAlign: A novel approach to correcting sample motion and 3D CTF in CryoET

TomoAlign is a software package that integrates tools to mitigate two important resolution limiting factors in cryoET, namely the beam-induced sample motion and the contrast transfer function (CTF) of the microscope. The package is especially focused on cryoET of thick specimens where fiducial markers are required for accurate tilt-series alignment and sample motion estimation. TomoAlign models the beam-induced sample motion undergone during the tilt-series acquisition. The motion models are used to produce motion-corrected subtilt-series centered on the particles of interest. In addition, the defocus of each particle at each tilt image is determined and can be corrected, resulting in motion-corrected and CTF-corrected subtilt-series from which the subtomograms can be computed. Alternatively, the CTF information can be passed on so that CTF correction can be carried out entirely within external packages like Relion. TomoAlign serves as a versatile tool that can streamline the cryoET workflow from initial alignment of tilt-series to final subtomogram averaging during in situ structure determination.

Pool boiling heat transfer enhancement by bi-conductive surfaces

The use of the bi-conductive surface provides a promising prospect for the enhancement of the boiling phase change heat transfer. In this study, a theoretical model of two-phase flow and boiling heat transfer on bi-conductive surfaces is developed. With the consideration of thermal conductivity contrast and conjugate heat transfer, the boiling behavior is numerically investigated based on a modified lattice Boltzmann method. The bubble dynamics during the boiling process on the bi-conductive surface are reproduced and the effect of the structural size of these insets on the boiling performance is explored. The results indicate that boiling performance is enhanced on the bi-conductive surface when compared to homogeneous ones. In-plane temperature variation on the surface contributes to the pinning effect on bubble contact lines, and thus promotes boiling heat transfer. Boiling enhancement gets optimized once the embedding pitch space equal to the capillary length of the boiling fluid. Increasing the width of the insets also improves the boiling heat transfer coefficient on the bi-conductive surface under low superheat conditions, but also leads to the advance of CHF. However, changing the depth of the insets shows almost no effect on the boiling heat transfer performance.

Dual-axis Volta phase plate cryo-electron tomography of Ebola virus-like particles reveals actin-VP40 interactions

Cryo-electron tomography (cryo-ET) is a pivotal imaging technique for studying the structure of pleomorphic enveloped viruses and their interactions with the host at native conditions. Owing to the limited tilting range of samples with a slab geometry, electron tomograms suffer from so-called missing wedge information in Fourier space. In dual-axis cryo-ET, two tomograms reconstructed from orthogonally oriented tilt series are combined into a tomogram with improved resolution as the missing wedge information is reduced to a pyramid. Volta phase plate (VPP) allows to perform in-focus cryo-ET with high contrast transfer at low-resolution frequencies and thus its application may improve the quality of dual-axis tomograms. Here, we compare dual-axis cryo-ET with and without VPP on Ebola virus-like particles to visualize and segment viral and host cell proteins within the membrane-enveloped filamentous particles. Dual-axis VPP cryo-ET reduces the missing wedge information and ray artifacts arising from the weighted back-projection during tomogram reconstruction, thereby minimizing ambiguity in the analysis of crowded environments and facilitating 3D segmentation. We show that dual-axis VPP tomograms provide a comprehensive description of macromolecular organizations such as nucleocapsid assembly states, the distribution of glycoproteins on the viral envelope and asymmetric arrangements of the VP40 layer in non-filamentous regions of virus-like particles. Our data reveal actin filaments within virus-like particles in close proximity to the viral VP40 scaffold, suggesting a direct interaction between VP40 and actin filaments. Dual-axis VPP cryo-ET provides more complete 3D information at high contrast and allows for better interpretation of macromolecule interactions and pleomorphic organizations.

Contrast Transfer Characteristics of Integrated Images Based on Optoelectronic Integration between Quantum Well Photodetector and Light Emitting Diod

The present study is concerned with overcoming the resultant image degradation due to the integration of the optoelectronics instruments (OEIDs). Accordingly, the characteristics of the image, due to optoelectronic integration, are handled and improved. The image features include the transmission mechanism and the concentration of electrons. The device performance is improved through the optimal design of the basic parameters. Furthermore, the efficient design of structure parameters will minimize the reabsorption process. Optimization of the integrator structure is realized. MATLAB environment is used for devising this instrument. The optimal number of integrator base and wave number characterizing the scale of near-infrared (NIR) image nonuniformity are estimated to be 13 and 0.206 respectively. The output of this instrument is also conducted through closed-form expressions of the underlined instrument. The achieved results show a remarkable accuracy for handling the deformations raised during the integration process. In addition, the results show that the carrier concentration changes the behavior of the output of the NIR image.

Accurate quantitative phase imaging by the transport of intensity equation: a mixed-transfer-function approach.

As a well-established deterministic phase retrieval approach, the transport of intensity equation (TIE) is able to recover the quantitative phase of a sample under coherent or partially coherent illumination with its through-focus intensity measurements. Nevertheless, the inherent paraxial approximation limits its validity to low-numerical-aperture imaging and slowly varying objects, precluding its application to high-resolution quantitative phase imaging (QPI). Alternatively, QPI can be achieved by phase deconvolution approaches based on the coherent contrast transfer function or partially coherent weak object transfer function (WOTF) without invoking paraxial approximation. But these methods are generally appropriate for "weakly scattering" samples in which the total phase delay induced by the object should be small. Consequently, high-resolution high-accuracy QPI of "nonweak" phase objects with fine details and large phase excursions remains a great challenge. In this Letter, we propose a mixed-transfer-function (MTF) approach to address the dilemma between measurement accuracy and imaging resolution. By effectively merging the phases reconstructed by TIE and WOTF in the frequency domain, the high-accuracy low-frequency phase "global" profile can be secured, and high-resolution high-frequency features can be well preserved simultaneously. Simulations and experimental results on a microlens array and unstained biological cells demonstrate the effectiveness of MTF.

Performance investigation of a two-stage sorption hydrogen compressor

Metal hydrides (MH) are widely investigated for several thermodynamic applications; sorption hydrogen compressor (SHC) is one among them. In this study, the thermodynamic performance and heat – mass transfer behaviour of a two-stage sorption hydrogen compressor (TSSHC) are investigated with the employment of La0·9Ce0·1Ni5 and MmNi4.8Al0.2 alloys in series. The hydrogen supply and the discharge temperatures are chosen as 20 °C and 80 °C, respectively. The thermodynamic performance data, i.e. compressor work and efficiency, are evaluated using the experimentally measured pressure-concentration-isotherm (PCI) and thermodynamic properties. In contrast, the heat and mass transfer behaviour is predicted by solving governing equations through the finite volume method (FVM). The numerical model is validated with experimental PCIs, and the results are in close agreement. The predicted cycle time is 75 min, comprising hydrogen supply, sensible heating and cooling, and hydrogen delivery. The TSSHC possessed a compression ratio of 9.5 and a cycle efficiency of 11.4% in which the hydrogen supply pressure is 9 bar using 0.5 kg of each alloy. Later, the influence of mass transfer on overall compressor work, heat input and efficiency is also presented.

Development and Evaluation of the Fourier Spectral Distortion Metric.

A spatial resolution metric is presented for tomosynthesis. The Fourier spectral distortion metric (FSD) was developed to evaluate specific resolution properties of different imaging techniques for digital tomosynthesis using a star pattern image to plot modulation in the frequency domain. The FSD samples the spatial resolution of a star-pattern image tangentially over an acute angle and for a range of spatial frequencies in a 2D image or 3D image reconstruction slice. The FSD graph portrays all frequencies present in a star pattern quadrant. In addition to the fundamental input frequency of the star pattern, the FSD graph shows spectral leakage, square wave harmonics, and residual noise. The contrast transfer function (CTF) is obtained using the FSD graph. The CTF is analogous to the modulation transfer function (MTF), but it is not normalized to unity at zero spatial frequency. Unlike the MTF, this metric separates the fundamental input-frequency from the other signals in the Fourier domain. This metric helps determine optimal image reconstruction parameters, the in-plane limit of spatial resolution with respect to aliased signals, and a threshold criterion for an image to support super resolution and reduce aliasing artifacts. Various sampling parameters were evaluated to optimize this metric and ascertain measurement accuracy. The FSD adequately compares resolution properties of 2D images and 3D image reconstruction slices for various x ray imaging modes without suppressing aliased signals.

Weld Defect Detection From Imbalanced Radiographic Images Based on Contrast Enhancement Conditional Generative Adversarial Network and Transfer Learning

When a sensor data-based detection method is used to detect the potential defects of industrial products, the data are normally imbalanced. This problem affects improvement of the robustness and accuracy of the defect detection system. In this work, welding defect detection is taken as an example: based on imbalanced radiographic images, a welding defect detection method using generative adversarial network combined with transfer learning is proposed to solve the data imbalance and improve the accuracy of defect detection. First, a new model named contrast enhancement conditional generative adversarial network is proposed, which is creatively used as a global resampling method for data augmentation of X-ray images. While solving the limitation of feature extraction due to low contrast in some images, the data distribution in the images is balanced, and the number of the image samples is expanded. Then, the Xception model is introduced as a feature extractor in the target network for transfer learning, and based on the obtained balanced data, fine-tuning is performed through frozen-unfrozen training to build the intelligent defect detection model. Finally, the defect detection model is used to detect five types of welding defects, including crack, lack of fusion, lack of penetration, porosity, and slag inclusion; an F1-score of 0.909 and defect recognition accuracy of 92.5% are achieved. The experimental results verify the effectiveness and superiority of the proposed defect detection method compared to conventional methods. For other similar applications to defect detection, the proposed method has promotional value.