WITHDRAWN: Evaluation of Spatial Performance in X-ray Imaging Detectors: CTF, MTF, LSF, and ESF Analysis

doi:10.21203/rs.3.rs-4557938/v1

This study was conducted at the University of Trieste's Department of Physics, focusing on the comprehensive characterization of the spatial response of an X-ray imaging detector. The primary objective was to measure and analyze the Contrast Transfer Function (CTF), Modulation Transfer Function (MTF), Line Spread Function (LSF), and Edge Spread Function (ESF) to evaluate the detector's performance.

Using a well-calibrated X-ray source, various test patterns and phantoms were imaged to acquire data. The CTF was assessed by analyzing the contrast response of the detector to a series of bar patterns with varying spatial frequencies. The MTF was derived from the Fourier transform of the LSF, which was obtained by scanning a narrow slit across the detector. The LSF provided detailed insights into the detector's response to a sharp line source. The ESF was measured by imaging a sharp edge, and subsequent differentiation yielded the LSF.

These measurements were conducted under controlled conditions to ensure accuracy and repeatability. The results highlighted the spatial resolution capabilities and limitations of the X-ray imaging detector, providing a detailed understanding of its performance metrics. This comprehensive characterization is crucial for optimizing detector design and improving image quality in various applications, ranging from medical imaging to industrial inspection.

Medical Physics

Contrast Transfer Function (CTF)

Edge Spread Function (ESF)

Line Spread Function (LSF)

Modulation Transfer Function (MTF)

X-ray beam

X-ray imaging detectors play a crucial role in a wide range of applications, including medical diagnostics, industrial inspection, and scientific research. The quality and accuracy of the images produced by these detectors are paramount for precise analysis and decision-making processes. The spatial response of an X-ray imaging detector is a key parameter that influences image resolution and clarity (Hasegawa, 1990).

Spatial resolution is the ability of an imaging system to distinguish between two closely spaced objects or details in the object being imaged. It is a measure of the smallest discernible detail that the imaging system can resolve (Yaffe, & Rowlands, 1997).

Spatial frequency is the rate of change of intensity or contrast in an image. It represents how rapidly the intensity or contrast of an image varies across space. Spatial frequency is often measured in cycles per unit distance, such as cycles per millimeter or cycles per pixel. For linear systems with real and even response functions, spatial resolution is fully characterized by the Modulation Transfer Function (MTF). When an imaging system has a high spatial frequency, it means that it is capable of capturing and resolving fine details (Cunningham, 2000).

To comprehensively understand and quantify the spatial response, several critical metrics are employed: The Contrast Transfer Function (CTF), the Modulation Transfer Function (MTF), the Line Spread Function (LSF), and the Edge Spread Function (ESF). Each of these functions provides unique insights into different aspects of the detector's performance (Dobbins & Samei, 2004).

Contrast Transfer Function (CTF)

The CTF measures the detector's ability to preserve contrast at various spatial frequencies, which is essential for distinguishing fine details in the image (Samei, et al., 1998).

Modulation Transfer Function (MTF)

The MTF describes the detector's response to sinusoidal input signals of varying spatial frequencies. It is a crucial metric for assessing the resolution and sharpness of the imaging system (Fujita, et al.,1992).

Line Spread Function (LSF)

The LSF characterizes the detector's response to a narrow line input, offering detailed information about its spatial resolution and the extent of signal blurring (Judy,1976).

Edge Spread Function (ESF)

The ESF is obtained by imaging a sharp edge and is used to derive the LSF. It provides valuable data on the detector's edge response and sharpness Boone & Seibert, 1997).

There are several techniques for measuring the MTF of an unknown sensor. The MTF can be measured from the image of a well characterized target, where knowing the spatial power spectral density (PSD) of the target enables the effects of the unknown system to be removed. Much success has been found using random targets (with known statistical behaviors) due to the relatively flat PSD and ease of system MTF identification (Daniels, 1997).

The MTF can also be obtained from measurements of the contrast threshold function (CTF) by using a Siemens Star target (Loebich et al., 2007) or a bar target (Boreman and Yang, 1995; Sitter et al., 1995). MTF measurement techniques may also involve measuring the line spread function (LSF) or edge spread function (ESF) (Park, and Z. Rahman, 1995).

The LSF is the derivative of the ESF, which is related to the MTF through a Fourier transform. MTF measurement methods utilizing the LSF ultimately depend upon how narrow of a line can be generated and, again, will depend upon how much signal is available through a small slit. The ESF measurement technique is perhaps the most common (Burns, 2000; ISO 12233:2017), due to its natural occurrence in imaging scenes, ease of fabrication of a sharp edge, and availability of large signal. Each of the above techniques have different experimental challenges and assumptions. In this correspondence we outline potential issues that can corrupt, contribute uncertainty, or introduce a bias into the calculation of the MTF for the ESF measurement method.

Understanding these spatial response functions is vital for optimizing detector design and performance. High spatial resolution and accurate imaging are essential in medical diagnostics for identifying small pathologies, and in scientific research for precise measurements and observations (Siewerdsen & Jaffray, 2000).

This study aims to perform a detailed characterization of an X-ray imaging detector by measuring its CTF, MTF, LSF, and ESF. Through these measurements, we seek to gain a comprehensive understanding of the detector's spatial response, thereby contributing to the enhancement of X-ray imaging technologies.

The Materials that has been used in this experiment are as follow.

1. X-ray Imaging Detector

o sensor S10811,

o CCD detector Hamamatsu,

o Signal processing unit C9266-03.

2. X-ray Source:

o X-ray tube with adjustable voltage and current settings.

o Tube voltage (25 KV)

o Tube current (25mA)

3. Test Patterns and Phantoms:

o Bar pattern phantom for CTF measurement.

o Slit phantom for LSF measurement.

o Sharp edge phantom for ESF measurement.

3. Computer with image acquisition software.

4. Slit camera:

o Acquire an image without X-ray -Dark current image,

o Acquire an image without sample -Flat field image,

o Position the bar pattern close to the detector and make sure it is well aligned with the pixel matrix,

o Acquire an image.

5. Additional Equipment:

o For precision stages in positioning phantoms and detectors.

o The collimators, Electrometer Keithley used for controlling X-ray beam shape and size (IEC, 2015).

7. Experimental Setup

o The X-ray imaging detector was positioned at a fixed distance from the X-ray source.

o Test patterns and phantoms were placed between the X-ray source and the detector.

o Collimators were used to shape the X-ray beam as required for different measurements.

Experimental conditions

This experiment was carried out in the physics laboratory of the Physics Department of the University of Trieste. The X-ray tube, which is the main device of the experiment, is located in a chamber. The chamber was not vacuumed, so there may be changes in the temperature inside the space and the general environment over time for the test. Still, this change, in this case, we can assume that it had a negligible effect on test.

According to Williams, et al., (2007), several safety measures must be considered for the X-ray tube to operate. First of all, all the windows of the chamber must be closed. Before switching on the X-ray tube, the "kV" and "mA" knobs on the external panel should be set to 0 (zero). Turning on the POWER on the external panel only after closing the chamber is possible.

After switching on the X-ray tube, we can enter the necessary parameters in the TUBE VOLTAGE/CURRENT field of the external panel (25 kV, 40 mA). It is mandatory to close the chamber windows to switch on the X-ray tube, and then the red light inside the chamber lights up which means the tube is on.

Before the acquisition, we can check whether the parameters have reached the desired value in the TUBE VOLTAGE/CURRENT field of the external panel, and then start the process. There is a SHUTTER button on the external panel to open the X-ray tube, and after we open it, the light falls on the detector and we can record the data through the Hamamatsu C9266DCamAPL software.

ORTEC 871 Timer and Counter is used to open and close the SHUTTER button for the required time interval to maintain the accuracy of the acquisition process and uniformity in the repeatability of the experiments. The acquisition process was set to 5 seconds, and the ORTEC 871 Timer and Counter should be set to 1 second. During the exposure time of the detector, we triggered the shutter so the X-ray beam was on for 1 second.

When installing and changing samples (bar pattern, line pattern, and edge pattern) during the experiment, it is necessary to turn off the X-ray tube, and after changing the sample, restart it. It is important to highlight that to measure LSF or ESF from data in ImageJ, we need to use the measurement line of ImageJ exactly at 90 degrees to get exact values. Additionally, the correct use of the timer during the experiment, waiting until the system is fully activated after applying the current and voltage is an important factor.

i. Measurement of Contrast Transfer Function (CTF):

o The bar pattern phantom was exposed to X-rays.

o Images were acquired at various spatial frequencies.

o The contrast at each spatial frequency was measured by analyzing the intensity profiles across the bars.

o CTF was calculated as the ratio of the image contrast to the object contrast for each spatial frequency.

ii. Measurement of Modulation Transfer Function (MTF):

o The slit phantom was used to obtain the Line Spread Function (LSF).

o A narrow slit was imaged, and the intensity profile perpendicular to the slit was recorded.

o The LSF was obtained by plotting the intensity profile.

o The MTF was derived by taking the Fourier transform of the LSF.

iii. Measurement of Line Spread Function (LSF):

o The slit phantom was scanned across the detector using a precision stage.

o Multiple images were acquired to improve signal-to-noise ratio.

o The LSF was determined by analyzing the spread of the line profile.

iv. Measurement of Edge Spread Function (ESF):

o The sharp edge phantom was imaged to obtain the ESF.

o The edge response was recorded by capturing the intensity profile perpendicular to the edge.

o The ESF was plotted and differentiated to obtain the LSF.

v. Data Analysis:

o Images were processed using image analysis software.

o Profiles for CTF, MTF, LSF, and ESF were extracted from the images.

o Fourier transforms were computed where necessary to derive MTF from LSF.

o Statistical analysis was performed to ensure the accuracy and repeatability of the measurements.

vi. Validation and Calibration:

o The experimental setup was calibrated using standard procedures.

o Repeated measurements were taken to validate the consistency of the results.

o Calibration phantoms were used to ensure the accuracy of the spatial response functions.

This systematic approach ensured a comprehensive characterization of the spatial response of the X-ray imaging detector, providing valuable insights into its performance metrics.

I. Contrast Transfer Function (CTF)

CTF Measurement Results:
- The CTF was measured for a range of spatial frequencies using the bar pattern phantom.
- The results indicated a decrease in contrast transfer with increasing spatial frequency, which is expected due to the limitations in detector resolution.
- At low spatial frequencies, the detector maintained high contrast, while at higher spatial frequencies, the contrast diminished significantly.

Table 1

Estimation of CTF
INPUT			OUTPUT
Frequency (lp/mm)	minimum	maximum	modulation
0.1	0.006	0.824	0.987
0.15	0.012	0.817	0.971
0.25	0.018	0.813	0.956
0.35	0.030	0.800	0.929
0.50	0.052	0.783	0.875
0.70	0.078	0.750	0.812
1.00	0.104	0.720	0.748
1.40	0.135	0.681	0.669
2.00	0.173	0.653	0.581
3.00	0.210	0.595	0.478
4.50	0.253	0.551	0.371
6.00	0.270	0.520	0.316
8.00	0.281	0.473	0.255
10.00	0.289	0.440	0.207

To get CTF, a bar pattern was used, and images of it were taken in different positions ranging from 0.05lp/mm to 10lp/mm. Also, it is essential to subtract dark current and divide by a flat field to compensate for readout structured noise, X-ray beam structure, and detector response inhomogeneity.

Finally, with the ImageJ software, it is possible to plot the profile and obtain minimum and maximum values of input. Through these values, we obtained CTF using the formula below.

As spatial frequency increases, the value of modulation gets lower which is illustrated in Fig. 9. Finally, calculated CTF provides an approximate value of MTF, and a more accurate estimate for MTF can be obtained from the values of CTF by using the Coltman formula (Coltman,1954) and then now, turn to check the precise spatial resolution.

Graphical Representation:
- A plot of CTF versus spatial frequency demonstrated a typical decay curve, indicating the detector's ability to preserve contrast at different frequencies.

II. Modulation Transfer Function (MTF)

MTF Measurement Results:
- The MTF was derived from the Fourier transform of the LSF obtained using the slit phantom.
- The MTF curve showed the modulation depth as a function of spatial frequency, with higher frequencies experiencing greater attenuation.
- The detector exhibited a cutoff frequency beyond which the MTF approached zero, indicating the limit of spatial resolution.
Graphical Representation:
- The MTF curve provided a detailed view of the detector's frequency response, showing the degradation of modulation at higher frequencies.

As we mentioned, CTF is not exactly the MTF, so on the other hand, we can obtain LSF using a slit camera to calculate the MTF. We repeat the acquisition process as we did in CTF, but this time we install a slit camera instead of a barn pattern. The Fourier transform of LSF is equal to MTF. Theoretically, the narrower the LSF is the greater the MTF value which is shown in Figs. 10 and 11 respectively.

IV. Edge Spread Function (ESF)

ESF Measurement Results:
- The ESF was measured by imaging a sharp edge and recording the intensity gradient across the edge.
- The ESF curve displayed a smooth transition from low to high intensity, reflecting the edge response of the detector.
- Differentiation of the ESF provided the LSF, confirming the consistency of the measurements.
Graphical Representation:
- The ESF plot depicted the gradual change in intensity, and its differentiation yielded the LSF curve, which matched the LSF obtained from the slit phantom.

III. Line Spread Function (LSF)

LSF Measurement Results:
- The LSF was obtained by imaging a narrow slit and analyzing the intensity profile perpendicular to the slit.
- The LSF curve indicated the degree of blurring introduced by the detector, with a sharp peak at the center and gradual falloff towards the edges.
Graphical Representation:
- The LSF plot showed a Gaussian-like profile, indicating the spatial distribution of the line spread.

Table 2

Relation CTF, LSF, ESF with MTF
Test object/sample	Measured quantity	Relationship with MTF
Bar pattern	CTF	MTF ≈ CTF
Slit camera	LSF	MTF = \|𝐹𝑇(𝐿𝑆𝐹)\|
Absorbing edge	ESF	MTF= =\|𝐹𝑇 (\(\frac{\text{d}}{dx})\) ESF\|

Another practical method to calculate the MTF is an absorbing edge which gives ESF, then using it, we obtain LSF = \(\frac{\text{d}}{dx}\) ESF and MTF =|𝐹𝑇(𝐿𝑆𝐹)|. As before, the acquisition process is the same as others, but this time the sharp edge is taken as a sample (like barn pattern in CTF and slit camera in LSF). Specifically, in this process, ESF was plotted as an intensity against the number of pixels as shown in Fig. 12. LSF can be found from the derivation of ESF and is expressed as a plot of intensity against position which is drawn in Fig. 10. Finally, the Fourier transform of LSF is MTF (Fig. 13).

According to the Table 2, all theoretical relationships with MTF are proved in our experiment. For example, in the first experiment, CTF obtained with a bar pattern is approximately similar to MTF. In the second one, the Fourier transform of LSF obtained with a slit camera provides MTF. Finally, the Fourier transform of the derivation of ESF measured with the absorbing edge is also MTF. So, it is possible to obtain MTFs that are not the same quantitatively but results are similar, using all three different methods. In other words, the graph of the MTF, obtained with LSF and ESF should be nearly equal and they should be similar to the graph of CTF. Our experimental graphs satisfy this expectation and again confirm that the results are correct.

The technical purpose of measuring MTF is to determine the spatial resolution of the imaging system. It is obvious from the results that the imaging system is working sufficiently because according to information about the detector provided by the manufacturer, from electrical and optical characteristics of the detector resolution needs to be typically 20lp/mm or a minimum of 15lp/mm. The results of MTF in our experiments proved that when the value of MTF is equal to 0.1 (10%), spatial resolution is 15lp/mm.

Generally, from this laboratory work, it is obvious that the easiest and fastest way to measure MTF is by using an absorbing edge because it is straightforward to find an absorbing edge and measurement is carried out once. In terms of achieving MTF with a bar pattern, it is required to do several measurements and a bar pattern. Additionally, the measurement result will not be exactly MTF. Finally, to calculate LSF we need a slit camera which is not omnipresent equipment.

Spatial Resolution:
- The spatial resolution of the detector was determined from the MTF and LSF measurements, indicating the ability of the detector to resolve fine details.
- The cutoff frequency in the MTF curve provided a quantitative measure of the detector's resolution limit.
Performance Evaluation:
- The CTF results highlighted the detector's capability to maintain contrast at lower spatial frequencies, essential for accurate imaging of larger structures.
- The MTF provided a comprehensive assessment of the detector's response across a range of spatial frequencies, crucial for high-resolution imaging applications.
Consistency and Reproducibility:
- Repeated measurements showed consistent results, validating the reliability of the spatial response characterization.
- The agreement between LSF derived from ESF and directly measured LSF demonstrated the robustness of the experimental methods.

The characterization of the spatial response of the X-ray imaging detector through the measurement of CTF, MTF, LSF, and ESF provided a detailed understanding of its performance. The results indicated that the detector is capable of maintaining high contrast at lower spatial frequencies and has a well-defined resolution limit as shown by the MTF. The consistency of the measurements across different methods validated the accuracy and reliability of the characterization process. These findings are crucial for optimizing detector design and improving imaging quality in various applications.

The comprehensive characterization of the spatial response of an X-ray imaging detector through the measurement of the Contrast Transfer Function (CTF), Modulation Transfer Function (MTF), Line Spread Function (LSF), and Edge Spread Function (ESF) has provided significant insights into the detector's performance and spatial resolution capabilities.

Findings of the Experiment

The CTF measurements demonstrated that the detector maintains high contrast at lower spatial frequencies, which is crucial for the imaging of larger structures.
As spatial frequency increased, the contrast transfer decreased, highlighting the limitations in the detector's ability to resolve fine details at higher frequencies.
The MTF analysis revealed the detector's frequency response, with a clear attenuation of modulation at higher spatial frequencies.
The cutoff frequency, where the MTF approached zero, defined the detector's resolution limit, providing a quantitative measure of its spatial resolution.
The LSF measurements indicated the extent of blurring introduced by the detector, with a sharp peak at the center of the line profile and a gradual falloff towards the edges. This function provided detailed information about the detector's spatial resolution and the degree of signal spread.
The ESF measurements, when differentiated to obtain the LSF, confirmed the consistency and accuracy of the spatial response characterization.
The smooth transition in the ESF curve reflected the detector's edge response, which is critical for applications requiring sharp edge detection.

Recommendation

Based on the experience and insights gained from performing the experiment on the characterization of the spatial response of an X-ray imaging detector, the following recommendations are suggested to enhance the accuracy, efficiency, and overall quality of similar future studies:

Further research can explore advanced techniques for improving the detector's response at higher spatial frequencies and reducing signal blurring.
The methodologies and results can be applied to different types of X-ray detectors to standardize performance evaluation across various imaging systems.
Engage with colleagues and experts in the field for collaborative discussions and peer reviews of the experimental design and results.
Consider forming interdisciplinary teams to bring diverse expertise to the study, enhancing the depth and breadth of the analysis.

Conflict of Interests

The authors have no conflict of interest.

Financial Support

This study received no specific grant from any funding agency in the public or commercial sectors.

Acknowledgments

We would like to express our gratitude to the Department of Physics at the University of Trieste for providing the facilities and resources necessary to conduct this study. Special thanks go to Prof. Luigi Rigon for his lectures, invaluable guidance and support to perform the experiment.

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The authors declare no competing interests.

SupplementaryFile.pdf
Manual of the Experiment

WITHDRAWN: Evaluation of Spatial Performance in X-ray Imaging Detectors: CTF, MTF, LSF, and ESF Analysis

Status:

Version 1

Editorial Note

Abstract

Figures

1. Introduction

2. Materials and Methods

3. Results

4. Discussion

5. Findings of the Experiment

6. Conclusion

Declarations

Conflict of Interests

Financial Support

Acknowledgments

References

Additional Declarations

Supplementary Files

Status:

Version 1