Lensometer Simulator

LENS VERIFICATION LAB

Read the lens the way the instrument reads it.

A manual lensometer with an American Cross target. Turn the power drum up from high minus until the thin mire lines come to a sharp, unbroken focus, turn the axis wheel until the thin line runs unbroken, then take a second power reading on the thick lines. Slide the lens off its optical centre and watch Prentice’s Rule put prism on the rings.

±20D of power-drum travel

0.25D per drum step

1Δ per reticle ring

Guided practice

LENS DIFFICULTY

PROCEDURE

Guided mode walks the procedure one step at a time and unlocks each control as you reach it. Switch to Practice or Test for the free instrument.

Step 1 of 9

YOUR READING

First reading · thin lines: —
Axis at the first reading: —
Second reading · thick lines: —
Add: —
Your prescription: —

Bring the thin lines to a sharp focus, set the axis, then record.

MOUNTED LENS

NOTATION

Plus-cyl and minus-cyl describe the same lens; transposition converts one to the other. A sign difference against the box prescription is a notation difference, not a measurement error.

Instrument

MIRE STATE

EYEPIECE FOCUS 0.00 D

Focus the eyepiece on the reticle before you touch the lens. The reticle and the target sit on different optical conjugates — turning the eyepiece to sharpen a blurred target only hides your own accommodation.

Turn the power drum toward plus and watch the thin lines come to a sharp focus.

Axis wheel 000

Power drum −20.00

Prism 0.00 Δ

One set at a time. At the end point the thin lines are crisp and unbroken while the thick lines are still a broad soft band — that separation IS the cylinder.

AXIS

000

Fine axis

SPH

−20.00

Fine power

Lens table

Drag the lens disc, or use the sliders. The prism readout follows continuously.

DECENTRATION

Distance off centre 0.0 mm

Direction 0°

Eye

Which eye is mounted decides which way is nasal, and so whether a sideways displacement reads base-in or base-out.

PRISM

no prism

Prentice’s Rule

Prism (Δ) = decentration (cm) × power (D)

decentration — how far, in centimetres, the point you are reading through sits from the lens’s optical centre.
power — the lens’s power, in diopters, in the meridian the displacement lies along.
prism — the result, in prism diopters (Δ). One Δ is one centimetre of image displacement per metre of viewing distance, and one ring on the reticle.

Worked example from the reference: a −10.00 D lens read through a point 2 mm (0.20 cm) from its optical centre gives 10 × 0.20 = 2.00 Δ.

Your lens, right now

0.00 cm × — = 0.00 Δ

Centred: 0.00 cm × any power = 0.00 Δ. No base direction is named for a centred lens.

ZONE READ

distance · +0.00 add

Add = near reading − distance sphere, recorded as a plus value. Leave the axis wheel exactly where the distance reading left it.

Teaching note, not simulated here: when the distance power is beyond roughly ±6.00 D, real technique flips the lens and reads the FRONT vertex power for the add. This page always reads back vertex power.

MOUNT YOUR OWN LENS

SPH +0.00 CYL +0.00 AXIS 000 ADD +0.00 PRISM 0.00 Δ LENS ROTATION 0°

PRISM BASE

Ground-in prism sits at the lens's own optical centre. Slide the lens off centre as well and the two add as vectors — set them against each other and the reading falls to zero.

The procedure, written out

The full single-vision sequence from the reference dossier. Guided mode walks steps 3–8 of this list; the rest are set-up you do once per session.

Switch the instrument on and set a comfortable working angle.
With no lens in the holder, focus the eyepiece for your own eye: past clear toward plus, then slowly back, stopping the instant the target first comes clear. Wear whatever distance correction you normally wear, every time.
Confirm the target is sharp with the power drum on exactly 0 D. If it is not, focus the eyepiece again.
Place the spectacles on the table, temples away from you, both rims resting on the holder and the frame’s 180° line parallel to the reticle’s horizontal. Slide until the mire cross sits on the reticle centre — that is the optical centre, and it can be dotted there with a marking pen.
Run the drum to high minus, then turn back toward plus until the lines come to a single, undoubled focus. Record the reading with its sign.
If the thin and thick sets resolve at two different drum readings, the lens is spherocylindrical: resolve the thin set first and record its power and the axis-wheel reading, then continue toward plus and record the thick set’s power.
Report the result as Sphere Cylinder × Axis — or as sphere alone if no cylinder was found.
Check the prism on the concentric rings before you take the lens off the table.

For a bifocal, do all of the above on the distance zone, then raise the lens until the segment sits over the target, keep the axis wheel where it is, turn toward plus until the segment’s lines resolve, and record that reading. Add = segment reading − distance sphere, written as a plus value.

Glossary

Lensometer / focimeter / vertometer: The optical instrument that measures a lens’s back vertex power, cylinder axis, prism and optical centre.
Back vertex power: The reciprocal of the back vertex focal length — the power a lensometer actually measures.
Badal principle: Putting the target near the front focal plane of a fixed powerful lens keeps its apparent angular size roughly constant while the vergence leaving the lens changes.
Field lens: The fixed, powerful Badal lens, positioned so its focal point sits at the back surface of the lens under test.
Keplerian telescope: The astronomical-type eyepiece telescope, fixed at infinity, through which the operator judges whether the emerging light is collimated.
Doubling prism (biprism): The fixed element that splits the target image into two displaced copies, which coincide exactly only at correct neutralisation.
Neutralisation: Measuring a lens by finding the instrument setting that exactly compensates its power.
Power wheel / power drum: The graduated knob that moves the internal target along the optical axis, read directly in diopters.
Axis wheel: The knob that rotates the target to line it up with a principal meridian of the lens, read in degrees on the 0–180 ophthalmic convention.
Sphere lines: The thin lines of an American Cross target. Their convergence gives the spherical power — and the axis-wheel reading at that instant is the cylinder axis.
Cylinder lines: The thick lines. Their separate convergence, at a second drum reading, gives the power of the other principal meridian.
Mire: The target pattern — lines, dots or a grid — viewed through the instrument to judge alignment and focus.
Prentice’s Rule: Prism (Δ) = decentration (cm) × power (D): the prismatic effect of reading a lens away from its optical centre.
Prism diopter (Δ): The unit of prismatic deviation: one centimetre of image displacement per metre of viewing distance.
Base direction: Where a prism’s thick edge points, reported as base-in, base-out, base-up or base-down.
Decentration: The offset between a lens’s optical centre and the point the wearer actually looks through.
Add power: The extra plus power built into the near zone of a bifocal, trifocal or progressive lens — commonly +0.50 to +3.50 D.
Optical centre: The point on a lens through which light passes with no prismatic deviation.
Concentric prism rings: The reference rings on the lens-table reticle, each conventionally one prism diopter of mire displacement.
American Cross target: The manual-lensometer target built from perpendicular thin (sphere) and thick (cylinder) line sets.
ANSI Z80.1: The American national standard that sets the tolerances a finished spectacle lens must meet.

What this simulation is, and is not

This is a teaching simulation of a manual lensometer with an American Cross target. The doubling prism’s displacement-per-diopter and the drum’s millimetres-of-target-travel-per-diopter are display calibration constants, not measured physics: the research dossier could not confirm either against a citable primary source, and both differ by instrument model. The ANSI Z80.1 tolerances quoted here come from trade-press summaries of the paid standard, not from the standard itself, so treat them as teaching tolerances. Prentice’s Rule, the 1 Δ per reticle ring convention, the ±20 D / 0.25 D drum and the +0.50 to +3.50 D add range are taken from the dossier. No reading taken here substitutes for a real instrument. Everything on this page traces to the lensometer reference dossier — see Sources at the foot of the page.