Li kontrolas la fokuson de la objektivo tra filtrilo.

Because fokuson is the direct object of kontrolas.

In Esperanto, the direct object usually takes the accusative ending -n:

• Li kontrolas la fokuson. = He checks the focus.

Here, li is the subject, kontrolas is the verb, and la fokuson is the thing being checked.

Because de la objektivo is not the direct object. It is a prepositional/genitive-style phrase meaning of the lens/objective.

So the structure is:

• la fokuson = the direct object
• de la objektivo = a phrase describing which focus

In other words, he is checking the focus, and that focus is of the lens/objective.

Here de means of.

So:

• la fokuso de la objektivo = the focus of the lens/objective

Esperanto often uses de where English uses of, possession, or a noun modifying another noun.

Examples:

• la pordo de la domo = the door of the house
• la koloro de la ĉielo = the color of the sky

La is the definite article, meaning the.

So:

• la fokuson = the specific focus
• la objektivo = the specific lens/objective

But tra filtrilo means through a filter, with filtrilo left indefinite.

Esperanto has no indefinite article like English a/an. So:

• filtrilo can mean a filter or just filter in a general sense
• la filtrilo would mean the filter, a specific one already known from context

Not exactly. This is an important false-friend issue.

In Esperanto, kontroli often means:

• to check
• to inspect
• to verify
• to examine

It can sometimes overlap with English control, but very often it is closer to check than to exercise control over.

So in sentences like this, kontrolas is best understood as checks or examines.

Objektivo usually means an optical objective, especially a camera lens or a microscope objective.

It is more technical than a general word like lenso.

A learner might compare:

• lenso = lens in a broad sense
• objektivo = objective/lens assembly, especially in optics or photography

So this sentence sounds like it is talking about equipment such as a camera, microscope, or similar optical device.

Tra means through.

So tra filtrilo suggests looking, passing, or operating through a filter, as if the filter is something between the viewer/device and what is being observed.

Per means by means of / using. In some contexts, per filtrilo might also be possible, but it gives a slightly different idea:

• tra filtrilo = through a filter
• per filtrilo = by means of a filter, using a filter

In this sentence, tra is natural if the idea is optical or physical passage through the filter.

Filtrilo is a nice example of Esperanto word-building.

It breaks down as:

• filtr- = filter-related root
• -il- = tool/instrument suffix
• -o = noun ending

So filtrilo literally means a filtering tool/device.

The suffix -il- is very common:

• tranĉi = to cut → tranĉilo = knife
• skribi = to write → skribilo = writing instrument
• filtri = to filter → filtrilo = filter

Because -as is the Esperanto ending for the present tense.

Basic verb endings are:

• -as = present
• -is = past
• -os = future
• -us = conditional
• -u = command/wish
• -i = infinitive

So:

• kontrolas = checks / is checking
• kontrolis = checked
• kontrolos = will check

Yes, Esperanto word order is fairly flexible, mainly because the -n ending helps mark the direct object.

The neutral order here is:

• Li kontrolas la fokuson de la objektivo tra filtrilo.

But other orders can be possible for emphasis, for example:

• Tra filtrilo li kontrolas la fokuson de la objektivo.

That said, for learners, the standard subject–verb–object order is usually the safest and clearest choice.

Because in Esperanto the definite article is always la. It does not change for case, gender, or number.

So you get:

• la fokuso = the focus
• la fokuson = the focus as a direct object
• la objektivo = the lens/objective
• la objektivoj = the lenses/objectives

The noun changes when needed, but la stays the same.