The essential distinction between SDTV and HDTV is bound up in the core issue of the term “high definition”. It implies that HDTV is distinguished from traditional video primarily by more “definition” – thus producing much higher picture sharpness. Thus, any discourse on mixing SDTV products with HDTV products needs to be closely examined from the viewpoint of its impact on the “high definition” aspect of the final imagery.

Unlike the digital cameras and recorders that make up contemporary digital imaging systems, the lens is a quite totally analog technology. It is a very physical technology – in the fullest sense of the word. The lens is also dynamic – in terms of the quite substantial degree of control it can exercise over the object image that it presents to the camera image sensors. But, those variations in light level, focus, and focal range offered by the lens come with some technical penalties.

As this paper is intended to examine “definition” the focus will be on the behavior of lens resolution. It is useful to establish some metrics – in optical terms – for picture “definition”. Audio and video systems (such as a television camera) are described by considerations of bandwidth and the specific system responses over the frequency ranges encompassed within their respective bandwidths. A similar approach can describe the resolution performance of a lens.

Optical Bandwidth
Lens Contrast and Resolution are inextricably intertwined. A series of closely spaced alternating black and white lines are visually distinguished by their relative contrast to each other. As their thickness and spacing are progressively reduced our human visual system is tasked to distinguish between these alternating lines. At some point we fail to do so and they blur into a gray patch. The same thing occurs as the test chart object scene passes through a lens. As the alternating lines increase in spatial frequency their optical representation by the lens will exhibit a progressive roll-off as simplistically illustrated in Figure 1. In other words, the contrast reproduction capability of the lens is modulated as a function of the fineness of detail of the alternating black and white lines. This particular representation of the lens output is technically termed the Modulation Transfer Function – or MTF. The horizontal axis represents the spatial frequency (increasingly fine detail from left to right) in Line-pairs per millimeter (Lp/mm). The vertical axis is the contrast (amplitude of black to white) of the optical image output of the lens.

Correlating Optical Bandwidth with Video Electronic Bandwidth
Any given television system is bounded by a finite electronic bandwidth – generally prescribed by specified digital filters – such as the 5.5 MHz specification for SDTV and the 30 MHz specification for both the 1080/60i and the 720/60p HDTV systems. These in turn define the maximum horizontal resolution – specified in Television Lines per picture height (TVL/ph) – that can be sustained by each of the three systems. Those TVL/ph specifications mathematically correlate with the optical Lp/mm in the manner depicted in Figure 2.

This tells us that an SDTV lens should have a high resolving power from 0 to 31 Lp/mm if it is to deliver imaging information that will fulfill the resolution capabilities of that camera. The optical manufactures strive to keep the MTF curve as high as possible over that range of 0 to 31 LP/mm. Beyond that they don’t care too much.

The 1080-line HDTV standard specifies that the camera must be capable of resolving 872 TVL/ph. This in turn translates to 82 Lp/mm – as depicted in Figure 2. The design goal of the lens designer is to maintain as high an MTF as possible across the 0 – 82 Lp/mm optical bandwidth in order to fulfill the capabilities of the HDTV camera.

Lens Resolution Considerations
First, it should be noted that the optical bandwidth requirement of the HDTV lens is x 2.7 that of the SDTV lens. Second, the HDTV lens produces a significantly higher MTF across that HDTV spatial frequency range. To achieve this higher degree of optical performance many facets of the optical design process must be carefully mobilized. The materials that comprise each and every lens element (a typical HDTV studio lens might have 35 separate glass elements) must be carefully chosen; the computer-aided design that is mandatory in their individual design becomes more sophisticated; and the manufacturing tolerances involved in accurately implementing that design are many times greater than in the case of an SDTV lens.

Additional Resolution Considerations.
In the spatial frequency region that lies beyond the required bandwidth of the SDTV lens the management of MTF becomes a very significant challenge indeed. Any minor deviations from the precision design of the lens elements will adversely affect the behavior of higher spatial frequencies. Manufacturing tolerances assume a whole new importance in attempting to optimize the resolving capabilities at those higher frequencies.

To get a “snapshot” of what becomes a truly complex optical phenomenon in the higher definition regions it is useful to examine the behavior of the two lens categories at a single spatial frequency midway between the boundary frequencies of the HDTV and the SDTV systems. This frequency is chosen to be 56 Lp/mm as shown in Figure 4. It is well within the passband of the HDTV lens – and accordingly lets us see how well the lens is managing the resolution behavior of the higher definition information. At the same time, it affords a view of how the SDTV lens is performing beyond the passband for which it was designed – providing a glimpse of how it behaves if tasked with resolving the same higher definition imagery.

Vagaries of Lens Resolution across the Image Plane
The earlier comparison centered about the MTF characteristic of an HDTV lens and an SDTV lens – when measured at picture center. The nature of optics is that resolution is at a maximum at the center of the lens elements – but then falls off from center to corner of the image plane. The rate of falloff is greater at the higher spatial frequencies. One method of profiling the lens MTF across the image plane is to look at two concentric rectangles (each with four corners – thus providing an 8-point locus). The inner rectangle is called the inner and the outer rectangle is called the “corner”. Figure 6 below shows how the MTF varies from picture center out to the corners of those two rectangles.

Vagaries of Resolution when Zoom Control is Exercised
The actuation of a zoom control moves two groupings of elements within the lens relative to each other. While implementing the desired change of focal length this action is also perturbing to a degree many attributes of the lens – specifically, the resolution or MTF, and a variety of optical aberrations. There is no eliminating these undesirable changes – design optimization merely reduces them to a degree. The HDTV lens design goes to extraordinary lengths to control these variations over the entire bandwidth of the lens. The SDTV lens does the same – but only over its much narrower bandwidth. Beyond its 32 Lp/mm extremity the designers pragmatically decline to add the sophisticated design attributes required for the HDTV lens. As a consequence, if a ‘spot” measurement at that central 56 Lp/mm spatial frequency is taken then a comparison between the unruly MTF behavior of the SDTV lens over the focal range of the lens can me made with the far better controlled HDTV lens – see Figure 6.

Vagaries of Resolution when Focus Control is Exercised
Many times in a shoot the camera will be sharply focused on a certain talent, who is then directed to move to another location in the set – with the lens angle of view kept constant (no change in the zoom control). But now the camera must be refocused on that talent in their new position. The MTF of a lens will not be identical between those two focus settings. That is, the MTF of the lens varies to a degree with object distance. Again, no attempt is made to control that variation in the “out of band” regions of an SDTV lens. Every attempt is made, however, to do so over the extended optical bandwidth of the HDTV lens. Typical relative behavior of a generic HDTV and SDTV lens will be as shown in Figure 7.

Vagaries of Resolution when Iris Control is Exercised
If one could design a truly perfect lens then finite limitations on resolution would still be imposed by the fundamental wavelength dependent phenomenon of diffraction. The end result would be the behavior of such a lens when the lens is continually stopped down (iris progressively closed) as shown by the straight black lines in Figure 8. In practice, no lens is perfect and there will be departures form this well-behaved system. Figure 7 gives an indication of the degree of departure of an HDTV lens and an SDTV lens at their respective f-4.0 setting.

Conclusion
The challenge to extend optical bandwidth and elevate MTF over the extended passband that defines high definition imaging is not trivial. It demands the very best in optical design, utilization of the highest quality materials for the optical elements, and significantly tightened control over tolerances in manufacturing. The unruly behavior of the SD lens in that higher spatial frequency range—for which it was never designed—can significantly impair the subjective picture sharpness as the normal operational controls of zoom, iris, and focus are exercised during production. The HD camera deserves the very best object image from its lens if it is to fulfill its role in true HD imaging. In that context, an SD lens should never be used on an HD camera. HD lenses, however, will improve the pictures created by SD cameras.