Objective
Choose a plausible generic objective starting point, or open Advanced parameters for exact catalogue values. EFL is the focal length of the whole objective as one equivalent lens; working distance is independent of it, and long-working-distance designs really do focus beyond their own EFL. Magnification is reported for a 200 mm tube lens. The equivalent plane sits inside the barrel so light focuses exactly one working distance past the front tip and the back focal plane (BFP) stays a real conjugate. Rated NA is the back pupil (2fNA): a beam filling it converges at the rated angle, and overfilling loses the overflow to the barrel. Pulse GDD uses a class-typical 30 mm N-BK7 equivalent that can differ by about 2x from a real objective.
Open in the canvas →In the real world
A real microscope or camera objective is a highly corrected assembly of many lens elements, not a single piece of glass — the element count exists almost entirely to cancel spherical and chromatic aberration, flatten the field, and reach a high numerical aperture without the image falling apart. Numerical aperture NA is the single number that matters most: it sets the objective's light-gathering cone and, through diffraction, the finest detail it can ever resolve, regardless of magnification:
Modern objectives are almost always infinity-corrected: a point at the sample (the front focal plane) emits a cone that leaves the back of the objective as a collimated beam, which a separate tube lens then focuses onto a camera or eyepiece — nothing focuses light directly behind an infinity objective on its own. The reference plane a focal length f behind the objective, on that tube-lens side, is the back focal plane (BFP) — where the objective's entrance pupil (radius above) is imaged. It matters most in laser-scanning microscopy: a scan mirror, or its relayed image via a scan lens and tube lens, is deliberately positioned at a plane conjugate to the BFP, so that as the mirror tilts, the beam pivots around a fixed point inside the pupil instead of walking across it — keeping the full aperture illuminated at every scan angle.
That same magnification formula is also why widefield imaging systems pick the objective focal length they do. A high-power compound-microscope objective (60×, 100×) has a very short effective focal length — often just a couple of millimeters — paired with a long tube lens. Its working distance, however, is a separate catalogue dimension: the axial clearance from the front boundary to the in-focus specimen plane. High-magnification objectives often have short working distances because of their practical optical and mechanical design, but working distance is not obtained from the magnification formula and long-working-distance objectives are specifically engineered exceptions. A stereomicroscope uses low-to-moderate magnification, a wide field of view, and enough working distance to get hands or tools under the lens; its zoom system can vary magnification without turning working distance into focal length.
One practical consequence of that pupil: the NA on the barrel is a ceiling, not a promise. You only work at the rated NA if your beam actually fills the back pupil. A laser beam narrower than the pupil converges at a proportionally smaller angle, giving a bigger focal spot and worse resolution than the label implies — which is why laser-scanning systems deliberately overfill the back aperture, accepting the power clipped off at the rim in exchange for the full aperture and the tightest spot the objective can make. Working distance, meanwhile, is a separate catalogue dimension set by the complete prescription. It is often shorter than EFL in high-power objectives, but there is no universal WD ≤ EFL rule for real compound objectives; specialized long-working-distance designs are the obvious exception.
In OpticalSetup
The inspector begins with a starting point grouped by immersion class — Dry, Water, Oil, and Long working distance — each offering the magnification and NA pairs people actually buy. They are plausible catalogue-shaped specs, not one manufacturer's prescriptions; choosing one sets EFL, working distance, medium, NA, and front aperture together. The labels carry NA and WD precisely because the two trade off: at a fixed magnification, every step up in NA costs clearance. Exact values remain editable in the collapsed Advanced parameters section, and any edit there drops the selector to Custom.
An objective here is set by three things you would read off a real catalogue — effective focal length (EFL), working distance, and rated NA — plus the front aperture that controls how big the nose is drawn. EFL is the focal length of the whole multi-element assembly treated as one equivalent lens, which is what "focal length" means on an objective; the inspector label spells that out. Magnification is not something you type in. It is reported from the EFL against a 200 mm reference tube lens, because magnification belongs to the objective plus whichever tube lens you actually place in the sketch, not to the objective alone. A fresh objective uses the 20× dry starting point: EFL 10 mm, WD 1.2 mm, NA 0.40, and 100% transmission.
Where the refracting plane sits, and why
OpticalSetup traces the objective as one equivalent refracting plane of focal length EFL, but it does not put that plane at the front tip. It sits one focal length short of the nominal focus — at the front tip plus WD − EFL — which for a real objective means somewhere inside the barrel. That single choice is what makes three things true at once:
- Collimated light from the tube-lens side focuses exactly one working distance beyond the physical front tip, so the drawn focus is the working distance you typed.
- The plane still carries the objective's real focal length, so an external 200 mm tube lens really does produce the reported magnification rather than a decorative label.
- The plane one EFL behind it is a genuine back focal plane (BFP): light focused there leaves the objective collimated. That is what widefield (Köhler-style) illumination needs, and it is the plane a laser-scanning relay has to image the scan mirror onto.
The BFP is drawn as a labelled marker next to the WD focus, and it is a traced conjugate rather than an annotation — put a source at it and the output really does come out collimated.
Working distance is not capped at EFL. Real long-working-distance objectives focus well beyond their own focal length — a 100× Plan Apo NIR reaches about 12 mm on a 2 mm EFL — by putting the equivalent principal plane ahead of the front glass, and the model reproduces that: when WD exceeds EFL the equivalent plane sits in front of the tip, exactly where the real one is. The only bound is a catalogue ceiling of 40 mm, or the objective's own EFL if that is longer, so older sketches that recorded WD equal to a long EFL keep their focus exactly where it was. Missing legacy values still fall back to EFL. Nothing is drawn at the equivalent plane — an objective is an opaque barrel, not a visible singlet. When a short working distance pushes the plane behind the default rear face, only the straight rear section of the barrel lengthens; the tapered nose is fixed geometry.
Rated NA is a real aperture, not a label
The back pupil has diameter 2fNA and is the objective's aperture stop. A beam that fills it converges at the rated angle: raise NA and the focusing cone opens, lower it and the cone closes. Nothing else in the objective sets the cone, so NA is a control rather than a caption.
That stop sits at the back focal plane, where an infinity objective's entrance pupil belongs, and this is what makes relaying a scan mirror onto the BFP marker do real work: a beam pivoting there stays centred in the pupil at every scan angle and loses nothing, while a pivot anywhere else walks across the pupil and is cut. (The single-plane model can push the BFP further back than any plausible barrel; the stop is then clamped into the housing rather than left blocking light in mid-air behind it, so the zero-walk property degrades for very long focal lengths.)
The metal around that opening blocks. Overfilling the back pupil is normal laboratory practice — it is how you actually reach the full rated NA — and the overflow is genuinely lost, so the objective reports what it costs. Two readouts sit under the NA control:
- Back-pupil fill — the beam diameter arriving, the pupil it has to get through, and a first-order estimate of the fraction that survives. That estimate is the area ratio for a uniform round beam, so doubling the fill costs about three quarters of the power.
- Effective NA in use — underfilling does not merely waste the rating, it hands you a smaller NA and a correspondingly wider focal spot. Fill half the pupil and you are running at half the NA; the readout says so, and by how much the spot widens. Overfilling is capped at the rating: you cannot buy more NA than the objective has.
A large 2fNA makes the housing physically wider rather than silently clipping at the drawn outline, and the dark bars across the barrel's rear face show the pupil diameter the beam has to fit through.
Medium and acceptance angle
The objective owns its medium; there is no separately placeable liquid component. Dry/air caps rated NA at 0.85 — the practical ceiling for real dry designs, rather than the physical n = 1 limit — water at 1.27, oil at 1.49, and a custom medium at the lesser of its index n and 1.49. The medium's index and the rated NA give the object-side half-angle θ = asin(NA/n) shown as a readout; changing medium may clamp an out-of-range NA but never changes working distance. Alongside the pupil, the tracer also rejects object-side rays steeper than that half-angle. Show acceptance angle — off by default, because most sketches want a plain barrel — draws it as a dashed sector at the actual contact or nominal focus.
Water, oil, and custom objectives derive a non-selectable immersion bridge to the nearest compatible contact in front: a Sample, a Sample on piezo stage, or a facing fiber endpoint. The target is chosen from the authored geometry, so a scanning stage carries the same relationship while it remains aligned and in range, then disconnects instead of making the objective jump between nearby samples.
The bridge spans the objective's complete front aperture and the contacted specimen or fiber face. Two cubic Bézier curves bow inward between those edges to make a legible meniscus in the canvas and in SVG, PNG, and GIF output. This is an authored schematic, not a capillary-surface calculation. If no contact is available, no liquid is drawn. Older high-NA sketches that never recorded a medium remain explicitly unresolved until one is chosen.
Controls and markers
The blue resize handle changes the front aperture. EFL is intentionally an exact Advanced field rather than a free-drag canvas knob, and is bounded to 2–60 mm: 2 mm is a 100× objective, 60 mm a 3.3×, and past that an "objective" is simply a lens whose derived barrel and internal planes stop being drawable at any usable zoom. Editing working distance moves the refracting plane without touching EFL or the reported magnification; raising EFL leaves an already-configured working distance alone, while lowering EFL past it carries the working distance down with it. Toggle "Show focal points" (the ƒ button) or select the objective to see both marked planes: BFP on the tube-lens side and the nominal WD focus on the sample side.
When this objective sits between a pulsed laser and an illuminated photocurable-resin sample, its NA is one of the values OpticalSetup can hand off to the dedicated Two-Photon Lithography Lab, alongside the laser's wavelength, power, repetition rate, and pulse duration — see the inspector on a resin sample's stage.
For pulse reporting, the equivalent plane silently contributes 30 mm of N-BK7. This is a class-typical GDD estimate, not a prescription: real objectives can be roughly half to twice that value, and the estimate does not scale with NA, magnification, immersion medium, or barrel geometry.
The 200 mm reference tube length is a real, common convention (Nikon and Leica both design infinity objectives against 200 mm) but not a universal one — Olympus uses 180 mm and Zeiss 165 mm — and OpticalSetup doesn't model a manufacturer choice or a separate tube-lens element the way the standalone telescope pairs two real lenses; the reference length is used only for effective-focal-length metadata and the first-order pupil estimate; it does not define the trace boundary or focus map. Working distance is a saved property bounded by EFL in this model, not a value predicted by magnification, NA, or immersion medium: a real catalogue pairs them through the internal design and can include long-working-distance prescriptions that violate this simplified cap. The supplied high-power starting points do retain plausible sub-millimetre clearances. The equivalent lens plane and the back focal plane it defines are first-order stand-ins for a compound objective's principal plane and pupil, not the real internal conjugates: one plane cannot reproduce a real objective's aberration correction, field curvature, or the axial spacing of its actual groups. The pupil stop and NA clipping remain qualitative and do not model diffraction, aberration correction, internal stops, or polarization at high angle. The pupil is a paraxial stop in a thin-lens tracer, so a beam filling it converges at atan(NA) rather than the sine-condition asin(NA/n) that the rated half-angle readout quotes; the two agree closely at moderate NA and separate as NA approaches its ceiling. The overfill estimate is a uniform-beam area ratio, not a Gaussian truncation or a vignetting calculation. Dry objectives cap at NA 0.85, the practical ceiling for real dry designs rather than the physical n = 1 limit. The drawn meniscus does not solve wetting, contact angle, surface tension, volume, or gravity; it adds no refracting boundary and does not model cover glass, index mismatch, focal shift, or immersion aberrations. The fixed 30 mm N-BK7 GDD equivalent can be wrong by about a factor of two for a particular objective; detector readouts report the combined path total, while this page identifies which part of that total is only assumed.