Lens Resolution Simplified: Understanding the Ability to Capture Detail( Part 1 and 2_research and showcasing by Ehsan Aslani)

Introduction To Lense and DOF.

Resolution refers to the capability of an imaging system to capture and distinguish fine details in an object. It is measured by the smallest spatial detail the system can resolve. In simple terms, resolution determines how sharp and clear an image appears.

Sharpness and resolution are closely related but not the same. Sharpness is a perceived quality influenced by resolution and contrast. The human eye focuses more on the contrast between elements in an image, known as acutance, rather than the resolution itself. Thus, a high-resolution image with low contrast may appear less sharp than a low-resolution image with high contrast.The resolving power of a lens is a measure of its ability to differentiate between two closely spaced lines or points in an object. The better the resolving power, the smaller the minimum distance between lines or points that can still be distinguished. Several factors, such as optical and mechanical design, coatings, and glass quality, contribute to a lens's overall resolution.

?In the realm of digital cinema, lens resolution requirements are particularly demanding. Design considerations must account for optimal performance in capturing fine details. Unlike film projection, which reached an accepted standard long ago, digital cinema continually pushes the boundaries of resolution capabilities.

?The f-number of a lens is a mathematical ratio that relates its focal length (f) to the diameter of its aperture (D). It is denoted as N. To calculate the f-number, you divide the focal length by the aperture diameter.

?For instance, if a lens has a focal length of 100mm and an entrance pupil diameter of 50mm, the f-number would be 2. The aperture of a lens is represented as a circle, and its size is measured in terms of the radius (r). The area (A) enclosed by a circle is calculated using the formula A = πr2, where π is a constant approximately equal to 3.14159.

?When the diameter of a lens's aperture increases by the square root of two, the surface area of the aperture circle is doubled. This means that twice as much light reaches the camera sensor. Conversely, when the aperture diameter decreases in increments of the square root of two, the amount of light reaching the sensor is halved.

?To simplify the measurement of aperture settings, f-stops or T-stops are used. These stops are expressed as a function of the square root of two and are typically adjusted in one-stop increments. By adjusting the f-stop or T-stop settings, photographers and cinematographers can control the amount of light entering the camera and achieve the desired exposure.

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Aperture f-number Simplified Values:

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The f-number of an aperture is calculated using the mathematical formula N = √(2^x), where x represents the f-stop value. Here are simplified values for different f-stop settings:

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- f/1: Approximately 1.4

- f/2: Approximately 2.8

- f/4: Approximately 5.6

- f/5.6: Approximately 8

- f/8: Approximately 11

- f/11: Approximately 16

- f/16: Approximately 22

- f/22: Approximately 32

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These values represent common f-stop settings used in photography and cinematography. They indicate the relative size of the aperture and help determine the amount of light entering the lens.

?Even professionals can find it challenging to remember the specific numbers associated with aperture stops. This can lead to confusion and mistakes, especially for independent filmmakers who are handling their cameras on set. It's important to recognize that these numbers are the result of years of scientific research and trial and error.

?To make it easier to remember the standard stops, here is a suggestion: if we can count from 1 to 10 easily, we can memorize the common aperture stops.

?By associating the numbers 1 to 10 with the corresponding aperture values, we can simplify the process of setting the desired aperture on our cameras. This can help us achieve the desired exposure and effectively control the amount of light entering the lens.

MTF understanding?

Now, after all, you may be wondering what this is all about and why you should remember these numbers and mathematics. Well, cinema is all about capturing realistic images that can connect with potential audiences through empathy and evoke emotions. In my opinion, these are the most important aspects of cinema. Light plays a crucial role in bringing our subjects to life as it reflects off them and passes through the sensors, as I mentioned earlier. Now, if, as a cinematographer, we tamper with these numbers and believe that we are doing it right, the illusion of motion may become like a hallucination. It is essential for us to comprehend how light interacts with our medium, including lenses, sensors, and most importantly, the knowledge behind it all.Our eyes are highly efficient and remarkably powerful when it comes to perceiving light, surpassing any camera in terms of capability and effectiveness.Despite the advancements in AI techniques, particularly those developed by Sony, our eyes remain the most powerful elements in our bodies.Our eyes' exceptional power stems from the flexibility of their muscles, allowing them to adapt based on the light they perceive. It's important to note that I am specifically referring to light, contrast, and dynamic range in my article, and not colors. Color is a separate field of study with its own scientific principles and considerations, which are not covered in my current discussion.Contrast plays a key role in determining the sharpness of pictures. It is measured using a metric called modulation transfer function (MTF). The MTF of a lens is influenced by the amount of contrast in the scene. The scene being? photographed modulates in frequency and contrast. The lens attempts to accurately transfer that? information to the sensor, the ratio of the resulting reduction in contrast to the original scene? contrast is a mathematical function expressed as a? percentage; that percentage is the metric of MTF.?

Lenses consist of solid glass materials with a specific refractive index, securely held in place by metal surfaces within a metal cylinder. A lens typically comprises multiple glass elements with optical coatings, mechanical surfaces, and optical cements. The majority of glass lens blanks used in modern lens production come from either Ohara or Schott, two prominent glass manufacturers. The formulation of glass used in lens manufacturing today is more restricted compared to the past. In earlier times, from the 1940s through the 1970s, it was common to incorporate radioactive Thorium 232 (marketed as "rare earth") and lead (flint glass) into certain glass elements to modify the refractive index. However, due to EPA regulations, the use of lead in glass has been limited, and glass manufacturers now employ alternative additives like cadmium, boric oxide, zinc oxide, phosphorus pentoxide, fluorite, and barium oxide.

Lens elements have their edges painted, and the interior barrels are equipped with baffles and coatings to minimize internal light dispersion. Achieving 100% transmittance or a flawless lens is unattainable. The performance of a lens varies across the frame, with the center typically delivering better results compared to the corners. Assessing a lens solely based on its center portion would be incomplete. MTF is a measure that quantifies the ability of an optical system, such as a camera lens, to transfer details from the subject to the image sensor. It determines the lens's ability to reproduce fine details accurately, including the resolution, sharpness, and contrast of the captured image. The MTF factor is typically represented as a graph or a set of curves that illustrate the lens's performance across different spatial frequencies, ranging from low to high frequencies. These frequencies correspond to different levels of detail in the image, with low frequencies representing larger, more general features, and high frequencies representing smaller, finer details.

By analyzing the MTF curves, cinematographers and photographers can assess the lens's performance and make informed decisions about choosing the right equipment for capturing the desired level of detail and contrast in their shots. A lens with a higher MTF value and a flatter MTF curve generally indicates better performance in reproducing fine details and maintaining contrast throughout the image. Understanding the MTF factor is essential for cinematographers as it helps them optimize image quality, sharpness, and contrast in their cinematic compositions. When you're considering buying a new lens for your camera kit, it's important to have as much information as possible to make an informed decision. One thing you might come across while researching lenses is the Modulation Transfer Function (MTF) chart provided by lens manufacturers. While MTF charts can provide valuable insights into a lens's performance, it's important to note that they are not the sole factor in determining whether a lens is good or not. To help you understand MTF charts and use them effectively in your lens purchase decisions, here's an introductory guide on how to interpret these charts and consider their readings. The Importance of MTF Charts for Photographers MTF charts offer photographers a valuable tool for assessing a lens's performance in specific conditions by comparing them to an ideal, hypothetical "perfect" lens. Even the most meticulously designed lenses have inherent imperfections and aberrations that occur naturally in the glass. By learning to interpret an MTF chart, you can gain insights into a lens's sharpness across its entire frame, from the center to the outer edges. Lenses are designed in a way that makes the center of the image sharper and with better contrast compared to the edges. MTF charts have two axes: a vertical one marked from 0 to 1 as a percentage. The higher a point is on the vertical axis, the better the lens performs in that specific area.

S Factor and M Factor:

Lens MTF (modulation transfer function) is assessed by using grid patterns consisting of evenly spaced black and white lines at two different sizes: 10 lines/mm and 30 lines/mm. The MTF chart displays two sets of data: Sagittal and Meridional lines. Sagittal lines consist of line pairs that run along a central diagonal line, extending from the bottom left-hand corner to the top right-hand corner of the lens. On the other hand, Meridional lines are perpendicular to the central diagonal line. These square wave grid patterns are positioned at regular intervals to measure contrast and resolution, respectively. When examining MTF measurements, comparing the Sagittal and Meridional data is beneficial for evaluating lenses that may exhibit astigmatism.

The vertical axis of an MTF chart represents the light transmission of the lens, ranging from 0% to a maximum value of 100%. The horizontal axis measures the distance from the center of the lens to its farthest corner along the diagonal. The numbers along the horizontal axis indicate the distance in millimeters from the center to the edge of the lens. The contrast of Sagittal and Meridional line pairs at different points from the lens' center is read and plotted on the chart.This MTF chart includes measurements for both 10 lines per millimeter and 30 lines per millimeter. It displays four separate lines. Higher and thicker lines indicate better performance. Higher lines represent better contrast (10 lines/mm) or resolution (30 lines/mm), while a thicker line indicates consistent optical performance across the image, from the center to the edge. The red line at 10 lines/mm represents the lens' ability to reproduce low spatial frequency or low-resolution details. A higher and straighter red line indicates better contrast reproduction. The higher the line, the greater the amount of contrast the lens can reproduce. The blue line at 30 lines/mm indicates the lens' ability to reproduce higher spatial frequency or higher-resolution details.

In part 3 of this article, I will explain the effects of MTF on depth of field (DOF) and the challenges faced by cinematographers in achieving focus in cinema. Normally, this task is performed by highly skilled AC1 professionals with years of experience and extensive knowledge. Every shot captured by these iconic DPs involves dedication, perseverance, and a trial-and-error approach. It's important to remember that cinema is a constantly evolving medium, requiring us to continuously update our knowledge and adapt to changes. By doing so, we can safeguard our own lives and the valuable cinematic projects we work on. Who knows, in just a couple of years, all our existing knowledge and the need for mathematical calculations may change. For now, we must continue to explore and discover new techniques in this ever-changing field.

References: - Nilsén (2015) "Making sense of implementation theories, models and frameworks" Implementation science (2015) - Singh & Bhattacharjee (2021) "Optical Parameters of Atomically Heterogeneous Systems Created by Plasma Based Low Energy Ion Beams: Wavelength Dependence and Effective Medium Model" Frontiers in physics (2021) Brüllmann & d'Hoedt (2011) Brüllmann and D'Hoedt "The modulation transfer function and signal-to-noise ratio of different digital filters: a technical approach" Dentomaxillofacial radiology (2011) - (Prenosil et al., 2016; "Isotope independent determination of PET/CT modulation transfer functions from phantom measurements on spheres" Medical physics - Viallefont-Robinet et al. (2018) "Comparison of MTF measurements using edge method: towards reference data set" Optics express (2018) - Acciavatti & Maidment (2019) "Nonstationary model of oblique x‐ray incidence in amorphous selenium detectors: Transfer functions" Medical physics (2019)

References:

Acciavatti, R. and Maidment, A. (2019). Nonstationary model of oblique x‐ray incidence in amorphous selenium detectors: ii. transfer functions. Medical Physics, 46(2), 505-516. , D. and d'Hoedt, B. (2011). The modulation transfer function and signal-to-noise ratio of different digital filters: a technical approach. Dentomaxillofacial Radiology, 40(4), 222-229. , P. (2015). Making sense of implementation theories, models and frameworks. Implementation Science, 10(1). , G., Klaeser, B., Hentschel, M., Fürstner, M., Berndt, M., Krause, T., … & Weitzel, T. (2016). Isotope independent determination of pet/ct modulation transfer functions from phantom measurements on spheres. Medical Physics, 43(10), 5767-5778. K. and Bhattacharjee, S. (2021). Optical parameters of atomically heterogeneous systems created by plasma based low energy ion beams: wavelength dependence and effective medium model. Frontiers in Physics, 9. F., Helder, D., Fra?ssé, R., Newbury, A., Bergh, F., Lee, D., … & Saunier, S. (2018). Comparison of mtf measurements using edge method: towards reference data set. Optics Express, 26(26), 33625.