Wednesday / January 22.

    What the MTF? (Modulation Transfer Function)

    1.5 hours with Assessment – Optometry Australia IoE Quality Assurance | 1G in New Zealand | 1 CPE in Singapore | 3 CE in India | CPD Points Available Internationally (Check with your local authority)

    Dr Madeleine Adams

    Presbyopia multifocal intraocular lenses use ‘tricks of the light’ to increase the range of vision from that afforded by a monofocal IOL. In this article, Dr Madeleine Adams provides a simple primer, comparing the optical functions of these modern optical technologies.

    LEARNING OBJECTIVES
    On completion of this CPD activity, participants should:
    1. Provide definitions and simple explanations of optical terms frequently bandied around in descriptions of the functions of modern intra ocular lenses (IOLs),
    2. Interpret key figures used to describe an IOL’s optical function. e.g. Defocus curves, contrast sensitivity curves and modulation transfer curves, and
    3. Understand why the optics of certain IOL types influences the fit for each patient.

    In the past decade there has been an explosion of presbyopia correcting IOLs – multifocals, then extended depth of focus (EDOF), with varying mechanisms of action.1 None of these IOLs (yet) match a young human crystalline lens with its ability to change shape to focus at a wide range of distances.

    Diffractive optics with concentric rings, refractive optics, pinhole designs, and positive and negative spherical aberration are all commonly used to increase the depth of field beyond that afforded by monofocal IOLs. Ultimately, a fixed amount of light – ‘the light budget’ – enters the eye, and the IOLs can ‘spend’ a certain amount of that budget on each distance from the eye. To spend on one distance, it will necessarily have to ‘scrimp’ a little on another distance. Depending on the IOL design, this may induce undesirable photic phenomena, such as haloes and starbursts, which are effectively ‘wasted light’, and can be considered trade-offs for decreased spectacle dependence. These trade-offs can be measured and described using optical terms.

    Understanding how differing IOLs spend, scrimp, and trade light can assist in choosing the IOL that best matches an individual’s eye health and visual demands. It can also help in understanding why some people may not be happy with their vision following surgery with a certain IOL, even if they can read the Snellen chart well.

    Comparing Light Budgets of IOLs

    To assess and compare the optical function of IOLs, we can use clinical tests and optical bench tests. These tests allow us to see how each IOL spends the light budget, and the effect this has on distance, intermediate and near vision – including the quality of vision and the dependency on good illumination.

    Both clinical and optical bench tests provide important information on the potential suitability of an IOL. Clinical tests provide mainly subjective data from trials and real-world use. Optical bench tests are objective; they allow us to predict what the clinical performance might be. Aberrometry is more like an objective clinical test, where the optical performance is assessed in vivo, and will be covered in a further article.

    I will use some schematic diagrams based on real IOL data, to assist in explaining how to interpret these in clinical papers and studies.

    Clinical IOL Performance Tests

    Clinical tests are familiar terms as they reflect the tests frequently performed by eye care professionals. In clinical studies it is important that they are performed in a standardised manner, to allow better comparison of IOL performance.2 Clinical tests are subjective tests, and they will also be influenced by any defect in the eye or visual pathway such as tear film, macular or nerve dysfunction. That is why IOL manufacturers are very careful in their patient selection for clinical trials, and why ‘real-world’ data from practitioners may sometimes deviate from the trial results.

    Clinical tests of IOL performance commonly include:

    • Unaided distance visual acuity (UDVA) at 6m, intermediate (UIVA) at 63 to 80cm and near visual acuity (UNVA) at 40cm.3 In clinical trials, the unit usually is logMAR, but real-world data reporting often uses a Snellen equivalent.
    • Corrected distance visual acuity (CDVA), intermediate (CIVA) and near visual acuity (CNVA) at the same distances as above, with any residual refraction corrected.

    Using the difference between unaided and corrected acuity, the predictability of postoperative spherical equivalent refraction can be plotted.

    Contrast sensitivity is assessed using an instrument that standardises light levels e.g., the CSV-2000.4

    Subjective quality of vision, such as patient-reported visual disturbances (starbursts, haloes, and glare) can be assessed with validated questionnaires such as the Quality of Vision (QoV).5

    All the above can be tested in different light conditions – that is, photopic (bright light) and mesopic (dim light).

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    Defocus Curve Interpretation

    We can look at the defocus curves to clinically assess how an IOL is spending its light budget, i.e., how much light for each distance.

    So, are those defocus curves presented at meetings by IOL representatives the clinical visual acuity at near, intermediate and distance plotted on a graph? Well, no. Let me explain.

    When we measure visual acuity using near and intermediate charts in clinic, many factors can influence the results. These range from the external – such as difficulty in achieving an exact distance from the eye to the chart in every person, and standardising lighting conditions – to the internal or patient factors, such as reading speed and neural processing.

    To reduce the influence of these potential sources of error, the function of an IOL at different distances is usually represented by a defocus curve. Defocus curves are created by presenting a series of positive – and negative – powered lenses in front of a patient’s eye in standardised conditions, then measuring the degree of ‘defocus’ that is induced. This method is a more controlled means for evaluating visual acuity at various distances.

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    Figure 1. An example of a defocus curve, comparing a bifocal and a trifocal IOL.

     

    An example of a defocus curve is provided in Figure 1. To interpret the defocus curve:

    1. The x-axis represents defocus, with the unit dioptres (D) in 0.50-D increments, from +1.00D to -4.00D.
    2. The y-axis represents visual acuity, with the unit logMAR from -0.10 (~Snellen equivalent 6/4.5) to 0.6 (~5/24). On this chart, the higher the peak, the better the vision.
    3. On the x-axis, the number represents the dioptre of lens placed in front of the patient’s eye to cause a precise amount of defocus so the logMAR vision can then be recorded.
    4. Remember the formula for focal length: f = 1/D in metres. If the lens is 0 power, that is a plano lens, the image is at 1/0 = infinity, and this represents distance vision. A -2.5D lens is equivalent to 1/-2.5 = 0.4 that is, viewing the chart at 40cm. When looking through a -4.00D lens, it would be the visual acuity equivalent of 25cm.
    5. The graph compares the defocus curve between two different IOLs. Each line represents the mean visual acuity for a group of patients, where one group has a bifocal IOL implanted (green line) and one has a trifocal IOL (blue line).
    6. Comparing the bifocal and the trifocal for 0D and -2.5D, that is, distance vision and 40cm, you can see they have similar values, and that the visual acuity is close to 0 (~6/6). However, the trifocal IOL has a plateau-shaped IOL whereas the bifocal dips down between 0 and -2.5. This essentially means the intermediate vision between near and distance is better for the trifocal.

    Contrast Sensitivity

    The tricks of the light used to achieve more than one focus (spreading the light budget across different distances) will necessarily reduce the amount of light at each focal point. This influences the contrast of the image.

    Presbyopia-correcting IOLs will reduce contrast sensitivity to some degree, and so IOL studies will frequently publish the effect of the IOL on contrast. Certain conditions, such as glaucoma and age-related macular degeneration, can have significant contrast sensitivity deficits even with excellent visual acuity.6 A reduction in mesopic contrast sensitivity has been shown to be associated with a higher risk of motor vehicle accidents in older adults.7 Thus, the effect of an IOL on contrast is an important consideration, particularly in pilots and drivers.

    Contrast sensitivity is the ability to detect differences in brightness between an object and its background. It measures how well individuals can distinguish objects that may not have distinct edges or sharp boundaries, and see shades of grey, rather than the high-contrast black and white on Snellen visual acuity charts. Contrast sensitivity is a detection task. That is, ‘Can you see it or not?’, as opposed to an identification task like visual acuity, ‘Can you identify the opotype?’.

    Simply put, visual acuity tests keep contrast constant and change the size of the image (spatial frequency), whereas contrast sensitivity tests change both the contrast and the image size. Low spatial frequencies are wide gratings (bigger image) and high spatial frequencies are thin gratings (smaller image). The unit of contrast is cycles per degree (CPD), which indicates how many full cycles of contrast (pairs of light and dark) are present in a one-degree angle of their vision (at a set distance):

    Contrast = Lmax – Lmin / Lmax + Lmin (where L is luminance).

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    Contrast sensitivity is the inverse of contrast level. The higher the contrast sensitivity, the lower the contrast level at which the patient can detect a target. For example, if a patient can detect a grating at 1% contrast (which is called the contrast threshold), then the contrast sensitivity for this patient at that spatial frequency is 1/0.01 = 100). Most commercially available contrast sensitivity tests provide measures for four or five size spatial frequencies (gratings) (Figure 2). Each spatial frequency is presented at 8–10 contrast levels. This test is usually performed in different light conditions such as scotopic (cones only vision), mesopic (cones and rods vision) and with and without glare; as well as for near and distance vision. Mesopic with glare represents conditions similar to driving in the evening.

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    Figure 2. A clinical contrast sensitivity test using gratings at different spatial frequencies and contrast levels (vectorvision.com/contrast-sensitivity-background).

     

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    Figure 3. Contrast sensitivity comparing a multifocal IOL and a monofocal IOL in different light conditions.

     

    Contrast Sensitivity Curve Interpretation

    Contrast sensitivity is often presented as a curve, which plots the lowest contrast level detected for a specific size target. Figure 3 is an example of a contrast sensitivity curve, comparing the performance of a multifocal IOL and a monofocal in different light conditions. Each point represents the median of the contrast sensitivity for that group.

    1. The x-axis of the curve is for spatial frequency. Here there are four different spatial frequencies i.e., grating sizes. The y-axis is for contrast sensitivity – log units of CPD.
    2. The blue line represents the multifocal, the green line the monofocal IOL.
    3. It can be seen that contrast sensitivity was fairly similar between the IOL group in each light condition except mesopic with glare, where the multifocal had lower contrast at higher spatial frequencies.

    Subjective Quality of Vision

    Patient-reported visual disturbances ,such as starbursts, haloes, and glare can be assessed with validated questionnaires such as the Quality of Vision (QoV).5 The QoV consists of 10 items, each with three questions regarding the frequency, severity, and bothersome nature of the visual disturbance, resulting in 30 questions. Standardised photos are shown to demonstrate visual disturbances (Figure 4).

    The QoV uses Rasch analysis, so estimates are on a linear interval scale, not an ordinal scale. This means the QoV questionnaire can measure change in symptoms and can cope with omitted items.

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    Figure 4. QoV pictures from the Quality of Vision Questionnaire.

     

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    Figure 5. A schematic and photo of an optical bench to evaluate IOLs.10

     

    Optical Bench IOL Performance Tests

    These are sometimes referred to as ‘in vitro’ tests; the IOL is not implanted in a human eye but aligned on the optical bench. An optical bench is a piece of hardware that provides a linear track along which to mount optical elements, with precise alignment and measurement capabilities (Figure 5). These can be used to measure the optical properties of IOLs and assess their optical quality. Most clinics do not own an optical bench, so we rely on the reported data from the manufacturer, or from independent studies investigating the IOL performance. There are ISO standards for optical properties that have to be met for regulatory approval by bodies such as the Therapeutic Goods Administration (TGA).

    Optical bench measurements of IOLs commonly include:

    • optical power (the spherical and cylinder power of the IOL),
    • spectral transmission – light and UV transmission,
    • modulation transfer function,
    • Strehl ratio, and
    • Predictions of potential for haloes.

    We will focus on modulation transfer function and Strehl ratio.

    Modulation Transfer Function

    So, what the MTF?

    Modulation transfer function (MTF) is a term used to describe the ability of an optical system to retain the contrast of an object. For an IOL, to accurately reproduce the contrast and resolution of an object being imaged. A higher MTF value indicates better image quality and resolution. It is analogous to a high-resolution TV versus a pixelated low-resolution screen. The MTF is the ratio of relative image contrast divided by relative object contrast:

    Modulation transfer function = relative image contrast/relative object contrast.

    Looking at it another way, MTF is related to contrast sensitivity. The MTF evaluates the ability of an optical system to transfer spatial frequencies with high fidelity. Contrast sensitivity measures the ability of the human visual system to detect differences in contrast. So, while high MTF predicts high contrast, the clinical result depends on more than just the optical quality of the IOL. The ocular surface, the pupil size, the retina, optic nerve, and brain of the recipient all play a role.

    To understand MTF better, let’s look at the gratings shown in Figure 6. In this simple explanation, the word contrast means the difference in intensity with black being 100% intensity and white being 0% intensity.

    A grating is a perfect pattern of bold black lines and white lines. If we plot the intensity of this, it is a square wave. Between the black and white there is 100% contrast.

    However, when it is passed through an optical system such as an IOL, the image is necessarily imperfect, as no optical system is perfect due to diffraction and aberrations. Plotting the image of the grating produces a sinusoidal pattern – rather than vertically up and down, it curves up and down. That means that now on the image, between the black and white lines, there are degrees of contrast – it is not just black and white, there are greys, too. The difference in intensity between the black and white is the same as the grating, but there are greys between (see lower part of Figure 6).

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    Figure 6. Contrast sensitivity at low and high spatial frequencies through an IOL image.

     

    Now if we begin to space the lines in our object more closely (more line pairs per millimetre), we increase the spatial frequency. The sinusoidal curves then start to overlap, and the difference in intensity is reduced. Thus, contrast decreases for any optical system as spatial frequency increases. As indicated in Figure 6, for low spatial frequencies, the MTF is close to one (or 100%) and falls as the spatial frequency increases until it reaches zero – the image becomes a uniform shade of grey.

    Note that defocus has a profound effect on MTF. When in perfect focus, the MTF is high, and as spatial frequency increases, the MTF slowly decreases in a linear fashion (Figure 7). As the degree of defocus increases, the MTF becomes less linear and drops off increasingly precipitously.

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    Figure 7. Effect of defocus on modulation transfer function.

     

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    Figure 8. Modulation transfer function of four IOL designs.

     

    Modulation Transfer Curve Interpretation

    So, we know now that MTF is impacted by spatial frequency (line pairs per mm, or image size) and defocus. The MTF curve that you most commonly encounter in publications and meetings is fixed at a particular spatial frequency, so you can compare the MTF (contrast) at different degrees of defocus (Figure 8). To produce a curve like Figure 8 from Figure 7, the MTF value of lines one to five from a particular spatial frequency are plotted against defocus.

    MTF curves from bench testing of IOLs can be plotted for:

    • different pupil (aperture) sizes e.g., 3mm and 4.5mm,
    • different light conditions such as mesopic and scotopic, at a single wavelength or in a spectral range covering a finite band of wavelengths, and
    • degrees of induced tilt and decentration.

    These indicate how the IOL may perform in various real-life conditions.

    The Optical Bench for IOL Testing

    To test IOLs, an optical bench, which includes a model eye, is set up. Modern MTF testers of optical systems use a single illuminated slit, a cross or a pinhole (point) on an opaque background as the object, with a high-resolution charge couple device (CCD) camera) as a measurement detector. The set up is similar to that shown in Figure 5.

    A light source radiates light rays, which are collected into parallel beams by a collimator, and illuminates the target of interest – a cross slit for MTF measurement or a United States Air Force (USAF) target image. The light beams then enter the test IOL, which is placed in a model eye, containing saline with a refractive index of 1.336. The test IOL focusses the projected target at its focal plane, which is then captured by a measurement detector (an objective microscope lens and a CCD camera). The cross-sectional intensity profile of the cross image is then computed into the MTF values via the Fourier transform technique.

    The USAF image test is useful to qualitatively confirm the optical performance of IOLs; images of the USAF image test at different defocus levels are compared subjectively by the observer.

    Figure 9 shows USAF images demonstrating image quality for distance, intermediate, and near of a monofocal, bifocal, trifocal, and an EDOF IOL. The quality of the captured images corresponds with the peaks on the MTF curve in Figure 8.

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    Figure 9. 1951 US Air Force resolution test chart for four different IOL designs at near, intermediate, and distance.

     

    Modulation Transfer Function Curve Interpretation

    Figure 8 shows a graph comparing the MTFs of four IOLs, at a fixed spatial frequency and a pupil size of 3.5mm. They are represented by four different coloured lines: a monofocal (blue), a bifocal (dark blue), a trifocal (green), and an EDOF (red) IOL. The MTF is on the y axis and the defocus on the x axis. Observations are:

    1. For distance vision (defocus of 0), the monofocal has considerably higher MTF than the other IOLs. The monofocal has one peak, the bifocal two (one at 0 and one at -3, that is, near vision), and the trifocal has an additional smaller peak at -1.66, that is, intermediate. The EDOF has more of a plateaued peak and a gentle decline from distance to near.
    2. The area under the curve – the total light entering the eye – is the same for each IOL. As the trifocal is spreading the light budget across three focal points, the MTF is lower for each. This means the image quality will be slightly reduced for all focal distances. This corresponds to the USAF images for monofocal, bifocal, trifocal, and EDOF IOLs in Figure 9.
    3. The EDOF has a plateau as defocus increases. This affords more tolerance of a degree of defocus (that is, not hitting a plano target) as the drop off around each point is less steep; they have a larger ‘landing zone’.

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    Strehl Ratio for IOLs

    The IOL’s optical quality can also be referred to by a Strehl ratio (SR), a parameter for the assessment of the IOL’s optical quality over the span of all spatial frequencies.8-9 This is calculated by dividing the area below the measured MTF curve, by the area below the diffraction-limited MTF curve. That is, it is comparing the actual MTF to an ideal aberration-free system. As SR considers all the peaks and troughs and oscillations that occur on the MTF curve, so it reflects the overall optical performance. A perfect IOL would have a SR of 1.0; the smaller the SR value, the worse the optical quality.

    Prediction of Haloes

    Haloes are dim circles of light around a light source, which may occur due to refraction, diffraction, or ray aberration. In the case of IOLs, it usually results from a simultaneous projection of multiple foci by an IOL. The perception of haloes is a physiological phenomenon, but their likelihood can be modelled using various methods on the optical bench.10

    Conclusion

    Modern intraocular lenses include a variety of designs that can provide an extended range of vision with reduced reliance on spectacles. They achieve this through ‘tricks of the light’, spending their light budget on different focal distances. This necessarily means some compromise on image quality, even if almost imperceptible in the healthy eye. Increasing our understanding of the data presented in regulatory material by the manufacturers, as well as results from independent optical bench and clinical studies, will allow us to better assess the degree of compromise for each IOL. We can use this information in individualised IOL selections for our patients. 

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    Dr Madeleine Adams MB ChB BSc Hons PhD FRANZCO is an ophthalmologist specialising in cataract and lens surgery.

    Dr Adams trained in Queensland and undertook fellowships in Australia and overseas. She was awarded a PhD by the University of Melbourne for her research into age-related macular degeneration. Dr Adams is the founding director of Insight Eye Surgery with practices in Brisbane and Noosa, Queensland.

     

     

     

    References

    1. Adams, M., Cataract surgery in 2022: Extending the range. mivision April 2022.
    2. Reinstein, D.Z., Archer, T.J., Srinivasan, S., et al., Standard for reporting refractive outcomes of intraocular lens-based refractive surgery. J Cataract Refract Surg. 2017;43(4):435–9.
    3. Vargas, V., Radner, W., Allan, B.D., et al., Methods for the study of near, intermediate vision, and accommodation: an overview of subjective and objective approaches. Surv Ophthalmol. 2019;64(1):90–100.
    4. Vector Vision CSV-2000 [see further: vectorvision.com/csv1000/ accessed 29 Sept 2024].
    5. McAlinden, C., Pesudovs, K., Moore, J.E., The development of an instrument to measure quality of vision: the Quality of Vision (QoV) questionnaire. Invest Ophthalmol Vis Sci. 2010;51(11):5537–45.
    6. Xiong, Y-Z.K.M., Bittner, A.K., Virgili, G., et al., Relationship between acuity and contrast sensitivity: differences due to eye disease. Invest Ophthalmol Vis Sci. 2020;61(40).
    7. Owsley, C., Swain, T., Liu, R., et al., Association of photopic and mesopic contrast sensitivity in older drivers with risk of motor vehicle collision using naturalistic driving data. BMC Ophthalmol. 2020;20(1):47.
    8. Gatinel, D., Pagnoulle, C., Houbrechts, Y., Gobin, L., Design and qualification of a diffractive trifocal optical profile for intraocular lenses. J Cataract Refract Surg. 2011;37(11):2060–7.
    9. Rawer, R., Stork, W., Spraul, C.W., Lingenfelder, C., Imaging quality of intraocular lenses. J Cataract Refract Surg. 2005;31(8):1618–31.
    10. Carson, D., Lee, S., Alexander, E., Comparison of two laboratory-based systems for evaluation of halos in intraocular lenses. Clin Ophthalmol. 2018;12:385–93.
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